Rental car company charging $2k for damage found hours after return — no proof. Worth fighting?

Looking for advice from anyone who’s dealt with rental car damage claims with Avis.

A rental car was returned at an airport location after a very short rental (less than 24 hours). The return time was mid-afternoon.

The issue is that the rental company didn’t document any damage until nearly 2 hours later, after the car had already been returned and presumably moved. They’re now charging about $2,100 for rear bumper damage.

Some concerning details:
• No photos or documentation from the time of return.
• No records of who handled the vehicle after it was returned.
• No chain of custody between return and inspection.
• Photos were taken later in a garage, not at the return lane (they said it was because of weather. I looked up weather reports in the area – weather was sunny/no rain days before, day of, and days after my rental period).
• When asked for logs or handling records, they said they don’t maintain that information.

Their position is basically:
“The renter is responsible regardless of fault”

The claim has been formally disputed, but they’re continuing to push for payment and mentioned escalation/collections.

Questions:
• Has anyone successfully fought a claim like this?
• Does a time gap between return and inspection actually matter?
• Is it worth continuing to push back vs. letting a credit card company handle it?
• If it ends up in collections but is disputed, how serious is that?

Appreciate any insight—this situation feels questionable but not sure how far to take it.