I've parked in NYC garages at least 100 times (5+ trips/year from Boston for over 20 years) and never had a scratch, a dent, or any other experience worse than once or twice having to wait 15+ minutes for my car to be delivered. Always a valet garage, probably used about 20 or 25 different ones.
They are professionals and they are responsible for dents and scratches and you don't keep your job long if you are costing them money