The programme claimed that because there are more craters on the side of the Moon facing away from the Earth than there are on the side facing towards it, the Moon must therefore have intercepted the incoming bodies that caused the excess number of craters on the "far side", thus preventing them hitting the Earth and quite possibly wiping out all life, once and for all. Unfortunately, this line of reasoning is wrong at every point.
There are undoubtedly many more craters on the side of the Moon facing away from the Earth than there are on the side facing towards it. However, the majority of the cratering on the inner planets and the Moon was caused by impacts from debris of various sizes during the period when the planets were forming from the dust and rock surrounding the Sun after it had initially come into being. This was relatively early on in the formation of the Solar System, when the number, size and orbits of the inner planets were more-or-less fixed but there was still a considerable amount of "left-over material" for them to either gather up by impact or eject from the system by gravitational interaction. The rocky inner planets were still only semi-solid at this time, hence the tendency for the impacts to form quite large craters and for material to "splash" off the surface. This would either fall back to produce the secondary crater chains so typical of the Moon or be propelled into space to constitute much of the non-asteroidal material which very [very!] much later would fall onto the Earth as meteorites.
After the majority of the material had either been gathered up, ejected or achieved a stable orbit of its own, the Solar System entered a brief period of consolidation as the planets "settled down", cooling sufficiently to gain a fully-solid surface and an atmosphere. This was the time when the rotation period of the Moon on its axis and its orbital period round the Earth became the same, due to the frictional effects of the "solid-tides" raised on the Moon by the then much closer Earth. Consolidation was followed by another intense storm of incoming material known as the Late Heavy Bombardment (LHB). It is not certain what caused this, but the best-established theory is that instabilities and resonances in the orbits of the outer planets caused Jupiter to move nearer to the Sun, deflecting asteroid-sized debris which had formerly been in stable orbits so that it moved towards the inner planets. Impacts were much heavier this time, as the impactors were larger, but not so frequent, as there were far fewer impactors. The craters formed were thus bigger than before (and so are often called "basins") but not so numerous.
After the LHB came to an end there began a long period of planetary evolution. All the inner planets were uniformly cratered at this time, as the impactors had arrived from all directions. This can still be seen in the case of Mercury, close-up pictures of which are very difficult to distinguish from those of heavily-cratered areas of the Moon. The Moon itself began to change, however, due to the continuing gravitational influence of the Earth on the still-solidifying Moon. The Moon's shape became distorted due to tidal effects and the distribution of the lighter and heavier rocks within it probably changed, resulting in a somewhat thinner mantle on the side facing the Earth. The distortions in shape (which varied continuously as the Moon went round in its elliptical orbit) caused local flexing and thus heating in the rocks nearer to the Earth, resulting in cracking of the thinner surface there and the formation of volcanoes. Lava spread out over the surface, filling extensive areas on the near-side to form the features known by the Latin name maria (literally "seas"). Because the lava obliterated large numbers of craters and basins, the total count decreased dramatically. This is the reason there are relatively more craters on the far-side than on the near-side: it is because, starting from equality, rather than additional craters being formed by numerous later impacts on the far-side in fact the total number on the near-side was reduced by the formation of maria i.e. there are not more craters on the far-side, there are fewer on the near-side!
It is, of course, true that impacts did not cease entirely after the LHB, but the number decreased dramatically: this can be shown by counting the number of craters on the maria, as clearly any crater here must be a relatively recent one, and craters with "rays" (material spread out around them) as the rays would be quite quickly degraded by further very small impacts and so they too must be recent (very recent, in fact). Such an analysis reveals that there was the occasional "Big One", such as the well-known ray-crater Tycho, but the size of such craters shows us that, on the whole, such impacts were relatively small. Detailed studies (e.g. Werner & Medvedev, University of Oslo, 2010) also show that, when corrected for a large number of factors which affect both the visibility and lifetime of ray-craters (which could skew the counts), there is no excess of ray-craters on the far-side of the Moon as compared to the near-side [see image below, which is centred on the middle of the near-side]. The only significant difference is between the side of the Moon facing "forward" along its orbit [left-hand side of image] and the side facing "backward" [right-hand side of image]. This is to be expected, as an impactor will strike the "leading edge" at a greater closing speed than it would the "trailing edge" and so the craters on this side will be larger.
The authors of this study state that at small Earth-Moon distances a "gravitational-lens" effect might focus incoming impactors on the near-side of each body, thus distorting the impact counts for the Moon. However, while the Moon was indeed much closer to the Earth soon after its formation, it initially moved away very rapidly and so was at substantially its current distance by the immediate post-LHB period. The lack of a near-side/far-side difference for relatively young craters may thus be taken as reasonable evidence that this situation would have held for the entire post-LHB period i.e. we may assume there has been no significant difference in cratering rates on the near and far sides from the time of the LHB up to the present.
We can thus see that the initial cratering period was at a time well before complex organic molecules could possibly have survived on the surface of the Earth and therefore a long time before the period when life could have emerged. It would thus have been irrelevant whether the Moon "intercepted" any incoming bodies destined for the Earth at this time because as there were so many of them a few less would not have made any difference, and of course there was nothing on the Earth to "wipe out" anyway! Later on, when life was emerging, the absence of a near-side/far-side cratering-rate difference shows that a shielding effect was not occuring. The apparent difference in cratering-rate implied by the present large difference in crater density is simply an artefact caused by the history of the Moon's development.
Even if one concedes that the Moon could act as a shield, calculation shows that the proportion of incoming impactors it might intercept is actually very small. If we make the generous assumptions that a) all incoming impactors will arrive approximately in the plane of the Moon's orbit, b) impactors will only arrive from outside the Earth's orbit, and c) the Moon will attract to it all bodies entering into the zone where its gravity exceeds that of the Earth, then the Moon will still only intercept a little over 6% of the impactors. This is because, although the Moon is a large body by normal planet/satellite standards, it has just 1/81 of the mass of the Earth. As relative gravitational influence varies as the square-root of the mass ratio, the gravity of the Moon will therefore only exceed that of the Earth if the impactor is 9 times as far away from the Earth as the Moon i.e. the Moon's influence extends for only 1/10 of the Moon-Earth distance (D). This will be on both sides of course, so the fraction of the half-orbit facing away from the Sun ["half-orbit" because of assumption b)] in which the Moon's gravity will dominate will be (2 x (1/10) x D) / (PI x D) = 0.064. As we have assumed all impactors will be in the plane of the orbit, this is also the fraction of them which will be intercepted by the Moon.
We know from geological evidence that the Earth was in fact struck by large impactors several times in the period when life was beginning. These impacts were (clearly!) not intercepted by the Moon, and to suggest that the small percentage of strikes that the Moon may have intercepted just happened to include all those which would have caused life to "stop in its tracks" is surely statistically highly implausible. Even if there might have ever been only one potential fatal strike (itself a highly unlikely hypothesis), I would suggest that 1 in 16 (at best) isn't good enough odds on which to base a "Guardian Angel" suggestion.
Finally, it is surely not reasonable to assume that, even if a given strike did disrupt life over a particular area, this would signal the permanent end to the genesis of all life on Earth. For instance, hydrothermal vents are considered a likely locus for the emergence of proto-life and they would probably be hardly affected by a strike. Also, as the emergence of life is now considered by many researchers to be more of a biochemical inevitability (given the right conditions) than a miraculous "one-off", even if a strike destroyed one attempt another would readily come into existence elsewhere. Indeed, recent research suggests that, far from being lethal to life, asteroid impacts were actually necessary, in order to establish the conditions conducive to life (Glikson & Vickers, Australian National University, 2006) and to bring in pro-biotic chemical species.
All-in-all then, there is absolutely no evidence that the Moon did protect (or could have protected) the Earth from "terminal" impacts in the period when the emergence of life was possible, nor that it has done so at any time from then until now.
