The bottom line here has nothing to do with AA's policy or OP's actions. It simply has to do with the well-taken suggestion that you ask and then wait at the counter while the agent makes entries in your PNR notes. AA won't provide a copy of those notes, but you can at least watch while the agent types away (perhaps doing a crossword puzzle).
While employees do not have the authority to vary the COC, some are certainly authorized to extend goodwill gestures and it is unlikely that AA would dishonor a small commitment such as this.
Without the PNR notes, this is a "he said-agent said."
Bear in mind for purposes of other situations that AA was obligated to provide a "duty of care" including hotels and meals at MIA, under EC 261/2004 because this was a departure from the EU. That duty applies in all circumstances having nothing to do with the "extraordinary circumstances" surrounding the LIS diversion.
In the end, passenger is no worse off. He had no reasonable expectation when he booked that he would be reimbursed and thus took the risk of non-reimbursement. This is not a situation where the passenger laid out cash on the promise of reimbursement.