You (not you personally) materially misrepresented to another that a rental was done by you and that you are entitled to mileage credit. In the process, you caused AA to take an action (reinstatement of forfeited miles) that AA would not otherwise have taken - resulting in a loss for AA. That's pretty much the definition of fraud.

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FRAUDULENT MISREPRESENTATION

THELAW.COM LAW DICTIONARY & BLACK'S LAW DICTIONARY 2ND ED.
A false statement or misrepresentation made intended that the listener will rely upon it and act upon it to their detriment.