How do I keep a car rental agency honest after I dented their car?
I hit a deer with a rental car but failed to purchase collision coverage.
There is a smashed taillight cover and some minor body damage.
How do I keep the car rental company (Fox) from charging me well above and beyond what an honest body shop would charge to fix the damage?

Make sure to read your rental agreement first. On a rental contract I had last year with Budget, when I looked it up, there is a paragraph in the contract that states:
"You understand that you are not authorized to repair or have the car repaired without our express prior written consent. If you repair or have the car repaired without our consent, you will pay the estimated cost to restore the car to the condition it was in prior to your rental. If we authorize you to have the car repaired, we will reimburse you for those repairs only if you give us the repair receipt."
Check first and if your contract says something similar, make sure to get their consent.
You can get 3 quotes for repair, so that you have some concrete evidence to argue, if they do not authorize you to fix the vehicle, and you feel that you’re overcharged for the repair.