The risk is that, in the simplest terms, AP has not been "paid" for the tickets, will eventually tumble to that fact, and cancel them. Why this may have occurred is irrelevant.
At a later date, the seats may not be available and that presents a whole series of other issues.
I would do a three-way call with Amex and AP and resolve this. Bottom line, if both are satisfied, you have obtained your tickets for free. But, it is rare that unpaid tickets remain live. At least with cash tickets, if there is an add/collect, you simply pay it.