Pathfinder lead developer/one of the lead developers made a ruling that it doesn't work. Used incredibly flimsy/no rules justification for it, so it's basically a "because I don't like the idea, that's why", but it's officially the intent for Pathfinder that Monks do not use INA and might have made it into an actual errata by now. (I suspect a similar negative answer would be given to any question regarding a PC taking a 'monster' feat.)