EC 261/2004 is clear. It applies to the operating carrier only. The operating carrier denying boarding (and causing delay) was IB. But OP did not have a valid IB ticket, so IB will deny the claim for denied boarding, delay, and duty of care as a valid denial of boarding. That is the way the Regulation is written.

AA was not the operating carrier and ---- if you accept the IB version as true ---- will likely make good on OP's reasonable expenses during the 24+ hours and may toss in some miles or a credit (but not cash) as a customer service gesture.

AA will likely respond to OP's claim, although it will likely take a good 30+ days. Hopefully it was a great deal shorter than the OP here as AA (and IB) both have all of the details.

For the benefit of others, it was indeed AA which needed to fix the ticket (presuming that IB is being fully truthful). While it should not be the passenger's job, it is absolutely the best practice to check your e-tickets and reservations after any change is made of any kind, whether it is made by the carrier or by the passenger. If the tickets were not properly reissued by AA, that would have been evident online (or by phone) and could have been fixed. The problem here was that the time to fix this ran out, The only time IB would be involved is if there were a valid ticket and IRROPS then occurred on the day of the flight. IB would then handle the reroute.