Sure, they could have a million dollars worth of coverage. But typically the deductibles are quite high. Their deductible could be $10,000, maybe $25,000. What this means is every claim is very costly. So they are strongly inclined to dodge, stall and avoid every damage claim attempt.
Valet parking companies generally have a lot of experience with handling customers who accuse them of inflicting damage on cars. So they have a large amount of practice in dodging claims. Most people are outmatched against an opponent like this.
Trusting that a valet parking company will be forthcoming about vehicle damage they caused is naive. In most cases, this isn't going to happen.
Some believe that if they are at a top property, like a 5 star type of property, they have nothing to worry about, and if an incident were to happen they would be well provided for. Well, the valet service is probably run by a third party vendor, and the workers are merely branded to appear to be employees of the venue.
Whether you are at a top property or not, expect it to be a struggle to get fairly compensated.
It is vital that you find any new damage before you ever pull away.
After you drive away, your chances of getting compensated for valet inflicted damage plummets to probably about 5%. It doesn't matter if it was dark and raining and you couldn't see the brand new dent. They will tell you that a fair determination of where the damage actually happened cannot be made, and your claim will be denied.
You must conduct a full vehicle damage assessment on the car before you pull away. This means carefully studying every square inch of the outside of your car — even the roof.
Don't feel rushed. You've got to VERIFY that they provided flawless service.
On-demand valet parking companies appear to be motivated to protect their reputations. I have gotten the impression they handle routine damage claims in a more consumer-friendly way. But you should still verify that no damage occurred BEFORE you part ways with an on-demand valet.