Do NOT turn this over to your insurance. This is a them problem, not yours. You should not pay anything for it, including through having your rates raised.

Tell Hertz to stuff it. Or use that time-honored phrase from every parking garage where anyone ever submitted a claim:

”We (I) find no evidence of damage caused by the renter (you).”

Finally, don’t rent from Hertz again. The once mighty outlet has fallen and is now NFG.