I occasionally rent and/or return from/to FBOs and, while it makes me nervous, ultimately rental records have been correctly charged though it often takes a while for someone from Hertz to pick up cars at the FBO, drive them back to their lot, and close out the rental, backdating where necessary.

(Pre-Covid I remember some larger FBOs having Hertz employees at a Hertz counter inside the FBO but I haven't seen any of these recently)

If you're hitting a brick wall with Hertz, call the FBO instead. FBOs are at least interested in customer service as opposed to Hertz who seems to actively hate its customers. You can certainly prove that you departed YIP on tail number N##### on date X at time Y.

Since the FBO has a contact at the local Hertz station that delivers cars and RAs from their main local lot to the FBO and back again, the FBO's reception desk/customer service staff all know how to get in touch with the local Hertz station. I'd work that angle. It will be a lot more fruitful than the Hertz run-around.