Does Naturalism Invalidate Epistemological Claims?

No.  Thomas Nagel's Mind and Cosmos has been receiving a number of reviews, most of them not positive.  The work has mostly been viewed as a member of those recent works which attack evolution by saying, Either we can know the world as it is, or our minds are the result of an irrational process like natural selection, but to claim that both can be true is either implausible or impossible. This is a false dichotomy.

In case people haven't noticed, our minds are not perfect proposition generating and evaluating machines, and at the very least we have working memory and speed-of-operation limits, not to mention all the blind spots and good-enough algorithms that you'd expect from a hand-me-down organ gradually accumulating change. Nagel is essentially arguing that trying to think with such a mess of tissue, we couldn't possibly know truth or observe these laws, or that our observation would necessarily be suspect. As to the latter, that's exactly why we've developed a method to check what we think we know (experiments). As to the former, we do seem to find ourselves in a universe that appears to be lawful and have objective truth, so how can we know that we're not just imagining things?

As a thought experiment - imagine you design a universe that does have laws and facts. You start it off with no self-aware entities, but allow natural selection. Over time thinking entities may develop. Yes, they will be imperfect, but purely for their own survival they may develop a basic ability to make limited predictions about how certain laws in their universe operate so that they can survive. And looking down over your creation one day, you notice one of them saying "we are limited and imperfect results of chance, how can we ever discern natural law"?

In point of fact I do not think that we can ever really know with absolute certainty we're seeing natural law or facts, but what we can observe and infer is good enough for our limited existence.