I am not familiar enough with the Objectivist epistemology to judge how it would answer this argument. I was tempted, at first, to write it off as a “stolen concept fallacy”, but there are parallels between it and Rand’s argument against determinism such that I can’t be certain how an Objectivist would rebut it. What follows is an excerpt from the argument that I think summarizes it accurately:
"If naturalism is true, there is no God, and hence no God (or anyone else) overseeing our development and orchestrating the course of our evolution. And this leads directly to the question whether it is at all likely that our cognitive faculties, given naturalism and given their evolutionary origin, would have developed in such a way as to be reliable, to furnish us with mostly true beliefs. Darwin himself expressed this doubt: “With me,” he said, the horrid doubt always arises whether the convictions of man’s mind, which has been developed from the mind of the lower animals, are of any value or at all trustworthy. Would any one trust in the convictions of a monkey’s mind, if there are any convictions in such a mind? The same thought is put more explicitly by Patricia Churchland. She insists that the most important thing about the human brain is that it has evolved; this means, she says, that its principal function is to enable the organism to move appropriately: Boiled down to essentials, a nervous system enables the organism to succeed in the four F’s: feeding, fleeing, fighting and reproducing. The principle chore of nervous systems is to get the body parts where they should be in order that the organism may survive. . . . . Improvements in sensorimotor control confer an evolutionary advantage: a fancier style of representing is advantageous so long as it is geared to the organism’s way of life and enhances the organism’s chances of survival. Truth, whatever that is, definitely takes the hindmost.
What Churchland means, I think, is that evolution is interested (so to speak) only in adaptive behavior, not in true belief. Natural selection doesn’t care what you believe; it is interested only in how you behave. It selects for certain kinds of behavior, those that enhance fitness, which is a measure of the chances that one’s genes are widely represented in the next and subsequent generations. It doesn’t select for belief, except insofar as the latter is appropriately related to behavior. But then the fact that we have evolved guarantees at most that we behave in certain ways–ways that contribute to our (or our ancestors’) surviving and reproducing in the environment in which we have developed. Churchland’s claim, I think, is best understood as the suggestion that the objective probability that our cognitive faculties are reliable, given naturalism and given that we have been cobbled together by the processes to which contemporary evolutionary theory calls our attention, is low. Of course she doesn’t explicitly mention naturalism, but it certainly seems that she is taking it for granted. For if theism were true, God might be directing and orchestrating the variation in such a way as to produce, in the long run, beings created in his image and thus capable of knowledge; but then it wouldn’t be the case that truth takes the hindmost."
Source: http://www.calvin.edu/academic/philosophy/…sm_defeated.pdf (pages 3-5)