It's not clear in the rules whether unarmed strikes are natural weapons. However, it seems plausible that if slam attacks are natural weapons, and can be improved with the Improved Natural Attack feat, then unarmed strikes can too. But, again, I think there is nothing in the rules that takes anything like a clear line one way or the other. Because this is the case, I think we ought to give FAQ rulings the normal authority for setting out what's in the RAW.
That said, I think it's certainly counter to the spirit of the rules to allow monks to improve their unarmed attacks with Improved Natural Attack. If the designers intended for (humanoid) monks to seriously consider the option of taking a feat to do more damage with their unarmed attacks, they'd have included the feat in the PH. Its presence in the Monster Manual instead suggests that it's mainly there for DMs to apply to monsters, even though, like all MM feats, it's possible for players to take it. The overwhelmingly plausible interpretation, here, I think, is that the technical availability, and usefulness, of Improved Natural Attack to monks exists only because of an oversight on the part of the designers. As such, it's a prime candidate for a house rule.