Sorry to hear about your "hoopdi". No offense, I drive a hoopdi too.
Here is the way I see it. UPS is liable. It is their responsibility to deal with the towing company ( and the towing compaines mandated insurance) as it was their actions that led to the damages. They have already acknowledged liabilty by paying the towing fee.
UPS is liable as they had a legally parked vehicle towed.
If it were me, I would get a mechanic to look at the 4X4. It should be easily determined whether the damage was caused by the towing. If it appears that way, get the mechanic to sign an affidavit stating his findings. I would then draft a letter, send it registered mail, along with the affidavit, to UPS.
Basicly the letter would be like this,
Dear Joe Thumb,
As you may be aware, UPS had my vehicle towed from your parking lot while I punched in on the clock. The vehicle is up to date as required by law. During the tow my 4x4 was damaged. Enclosed you will see an afidavit from a mechanic stating that the damaged was caused by the illegal tow. Being that UPS has acknowledged wrong doing by paying for the tow, I expect UPS to make me whole by paying for the repairs to my vehicle. I would be willing to get several estimates and we can agree to the cheapest option. I expect to hear back from you by the end of next week. If not, I will be forced to hire an attorney to look at all of my options.
.
UPS will either ignore you, deny you, or agree. I feel as though they would need to work out the financials with the towing company. You had no say in who towed your car. UPS is the one that had it towed by the company that they have a contract with.