IMO its all very well for AP to say you owe them.  But if they cannot/will not provide you with evidence of where you have allegedly underpaid, I would be personally  telling AP to go take a flying leap off a short pier.

No proof from AP, no debt for you - and if the debt collector does call, tell them you are waiting for AP evidence of alleged underpayment, yet to be received.

I dare say you may have made an error, but at the same time you are entitled to detailed proof of that error.  I certainly wouldn't just pay up and shut up - and don't be intimated by the threat of a debt collector.  It is firmly in AP's court to provide proof of their claim.