Reading this thread and the other one (theEvil's Poll on the same subject) has led me to change my mind.
Monks' unarmed attacks are treated as natural weapons for the purpose of spells and other effects. A feat is an effect. Therefore, a feat treats a monk's unarmed attack as a natural weapon. Therefore a feat's prerequisites treat a monk's unarmed attack as a natural weapon. Therefore a human monk with sufficiently high BAB qualifies for INA.
The key point of the argument is determining that a feat is an effect. What convinced me of this is the observation that a feat is a result of leveling up. The term "effect" is loosely enough defined that it is permissible to consider a "result" to be a kind of effect. I also hold that if a feat is an effect of leveling up, so are all the parts of a feat; in particular, any pre-requisites of the feat. The prerequisites are not the effect of a feat in the way that the benefits of a feat are, but they have to originate from something (the event that resulted in the feat is the most plausible origin), and so are the result/effect of something.
This interpretation of "effect" might lead to other problems, and so I might have to revise my opinion yet again, but this is where I stand at the moment. Specifically, if it makes the monk's unarmed attacks count as a natural weapon for all purposes, then there would be a problem; the rules on iterative attacks would kick in, etc.. But I don't see the rules governing iterative attacks as being an effect of anything, so they shouldn't kick in. And if they were an effect, then there remains the point that a monk's unarmed attacks are also considered manufactured weapons, and so the manufactured weapons rule could be followed if it was in the monk's best interests.

Monks' unarmed attacks are treated as natural weapons for the purpose of spells and other effects. A feat is an effect. Therefore, a feat treats a monk's unarmed attack as a natural weapon. Therefore a feat's prerequisites treat a monk's unarmed attack as a natural weapon. Therefore a human monk with sufficiently high BAB qualifies for INA.
The key point of the argument is determining that a feat is an effect. What convinced me of this is the observation that a feat is a result of leveling up. The term "effect" is loosely enough defined that it is permissible to consider a "result" to be a kind of effect. I also hold that if a feat is an effect of leveling up, so are all the parts of a feat; in particular, any pre-requisites of the feat. The prerequisites are not the effect of a feat in the way that the benefits of a feat are, but they have to originate from something (the event that resulted in the feat is the most plausible origin), and so are the result/effect of something.
This interpretation of "effect" might lead to other problems, and so I might have to revise my opinion yet again, but this is where I stand at the moment. Specifically, if it makes the monk's unarmed attacks count as a natural weapon for all purposes, then there would be a problem; the rules on iterative attacks would kick in, etc.. But I don't see the rules governing iterative attacks as being an effect of anything, so they shouldn't kick in. And if they were an effect, then there remains the point that a monk's unarmed attacks are also considered manufactured weapons, and so the manufactured weapons rule could be followed if it was in the monk's best interests.