American Airlines Refusal to Reimburse Hotel Cost After Overnight Delay, Contrary to Gate Agent's Advice Internet

My 9:25 flight from Philadelphia to Grand Rapids was delayed until 10:25 a.m. the next day (I think they said it was for "technical reasons").  When I asked the agent handing out meal vouchers about a hotel (I had flown in from Portugal earlier that day) the agent told me none of the airport hotels with which they had voucher arrangements had any vacancies (it was a Saturday night), but that I could make my own hotel arrangements and seek reimbursement from American Airlines.  I did.  What followed was a total run-around.  I filled out the reimbursement form on AA's website, waited a few weeks without hearing anything other than a robo-acknowledgement, then called and was told the form I filled out was only for ticket reimbursement and that I needed to talk to Customer Service.  I sent Customer Service an email and received back -- an apology.  Nothing more.  No information on how to seek reimbursement.  I have read online that American has a policy that reimbursement in my circumstances requires not just no vouchers availalbe, but "written approval."  That is not what the gate agent told me, however, and I made the arrangments to stay at the very expensive, very crappy airport Clarion hotel based on what I was told.