Chris Elliott to the rescue! From the article, published on MSNBC:
Instead of excuses, a Mandarin representative should have called you as promised to ask for the necessary paperwork [...] I think you could have handled this a little differently, too. Once you reached someone by phone, you should have immediately asked for an e-mail address for both the hotel and the valet company. Copying both parties on any future correspondence would have ensured that everyone had access to the case notes in the form of your previous e-mails.
You also overlooked two items. You might have asked the hotel if it would accept any other document besides a faxed or mailed citation. A credit card billing statement, an invoice or a citation number could have also done the trick. And second, you should have enlisted the help of your car rental agency in securing the necessary paperwork. (Government agencies are notoriously slow, but the odds are good that your agency has a copy of the document your hotel wants.)
In the end, Elliott ended up contacting the Mandarin on the guest's behalf and, as it turns out, they would accept a citation notice from the car rental company. After the guest faxed the notice to the Mandarin, she got a check for $85 and everyone lived happily ever after.