From the core rules themselves there are at least two equally valid viewpoints.
1. Read broadly, "effects" from the monk class description includes feats such as INA since effects is a undefined game term, in the general sense, and therefore inludes things that produce effects, such as feats, not just the effect itself and thus excluding feat prerequisites.
2. Read narrowly, "effects" is a very limited term. Feats have effects (or not, it matter not to this choice), but are not in and of themselves effects or, even if they are, the prerequisites for them are not.
I have a lot of trouble with number two, as it seems like an overly-technical reading that assumes an unreasonably high level of precision in the original writing of these rules.
In addition to the above, the PHB II and the FAQ both allow for INA for monks, so it seems that if you use sources outside the core rules (assuming you consider the FAQ and PHB II to be outside the core rules), then yes you should allow it per the rules. Whether or not the FAQ is part of the core rules is the subject for some debate.
There are other variations of how to look at the results, too, but, generally, that's about it.
Bottom line: some folks feel this is overpowered and/or not allowed by a very strict reading of the rules. WotC has taken the opposite view.
I don't know what else there is to say. You (or your DM) are now, I think, fully armed to make your own choice.