Grammar: May versus Might

So I was reading the other day and I came across a sentence which read, in part: "If he turned back now, he may..."

And I'm thinking, "may?"  That doesn't sound right.  I would've written "might" there.  I wouldn't call this a grammar peeve, exactly, because this is the first time I can remember coming across it.  But it got me to wondering if there was a rule.

Here is a good explanation.  In the case of the book I was reading, which shall remain nameless for now (but when I review it, I'm sure I will bring this up again, seeing as the author is an ENGLISH TEACHER), this is a hypothetical and therefore "might" is correct.

I would say that the only way to learn these things is to read a lot.  But the problem is that if you read some of the books I've been reading lately, you'd be learning stuff that wasn't correct.  Maybe it's better that I came to fantasy in my mid to late twenties, after I'd graduated from an Ivy League college.