I’ve not had the experience of going into a police station and reporting something like a bent steering wheel. I have no idea how that works, especially if there is a language barrier. (I had a very serious Carabiniere in MIlan who wanted me to erase pictures I had taken of a synagogue. While he spoke no English, his assault weapon was fluent in all languages.)
Here in Los Angeles police will not visit a non-injury accident. While I‘ve spoken to the police from time to time (and I have a monthly Zoom with our local officers), I can’t imagine what their reaction would be. Me: Officer, I’d like to report a bent steering wheel on a rental car, and I need a written report from you to give to the rental agency otherwise they will void the LDW coverage they charged me for. Cops: Laughter? Blank stares?
I think you have reached the end of the road of consumer advocacy. Has the damage been charged to your credit card? If not, you might think of closing that number or account and sitting back. Budget may indeed send the matter to collections. Collections might report it to the credit bureaus, or they might not. Collections might sue you, or they might not. The only reason to pay is to avoid the possible hit to your credit and to put this matter behind you.
To me, the question is not whether you bent the steering wheel. To me, the real question is how was Budget prejudiced by the failure to get a police report when the customer bought and paid for LDW, even if a term of LDW requires a police report.
Separately, do you think you could phone in a police report now, long distance? Maybe VI police are used to Budget’s rules? Or even fax in a report to the cops?