However, you all seem to be assuming that a Coup de Grace is simply attacking a helpless foe. Well, it isn't. A babboon is very likely to attack a helpless foe until it's dead- but what makes you think that's a Coup de Grace? A PC Fighter can attack a helpless foe until it's dead, and get huge bonuses on its attack rolls- but it isn't Coup de Grace-ing at all. Would a babboon, in the middle of a battle, refrain from attacking, to focus its strength into one strong, focused attack onto one vital point of its foe's anatomy, focusing its attention on this one point so much that it allows its other foes to get free attacks in (that is, would a babboon willingly incur attacks of opportunity)? Would a babboon be intelligent enough to do something like that?
Of course not. You are all confusing a Coup de Grace with attacking a helpless foe, which are two different things. An animal (or generally anything with an intelligence under 3) is never going to Coup de Grace while in a battle, because it requires the animal to take its attention completely from the rest of battle, incurring attacks of opportunity.