1. Do a chargeback and ask Amex to request the actual garage invoice as Hertz is only giving you a list of undocumented fees.
2. Expect no such invoice exists and for Hertz to send you a collection notice
3. Ask Hertz accounting again for the document in 1., above
4. Expect Hertz to not provide the document
5. Expect a collection agenc nasty letter
Rinse and repeat 3 and 4, above
6. Insist that without documented invoice there is no chargeable claim and ask the collection agency to close the file

Expect a lot of phone time and some unpleasant conversations and a 50/50 chance your chargeback will stick without damaging your credit score too much

I have done this on an undocumented Hertz claim for a wheel scuff and succeeded. I don't care about my credit score too much, so individual appetite for this will vary.