The company doesn't need to prove it made the repairs, just that the damages were sustained and what the cost of repairs would be

Whether the owner of the car chooses to get the damage repaired or not is up to them

It sounds like the damage was there on return and was not marked on the rental at pick up time ; that you think the damage is small doesn't matter .

The simplest thing is to pass it to card company, if covered for rental damage, and it can reimburse you and pursue Hertz if it has issues with the claim. No point having coverage and then worrying about it