If you want real deniability, you might want the service to include another driver that rides in with the car, drives the player's car home, puts it in park in the driveway, and then lets the player transfer back into their own car to slip it into the garage. And also some of those Russian anti-hangover pills.
(I'm not really suggesting that it appear that the player drove their own car home to outside observers; just that it would be weird and creepy to let some stranger park your car in your garage. It's mostly about not leaving a car parked in front of a bar the next morning.)
There's a service in my city that does this for 30 or 40 bucks depending on how far they have to go. Minus the hangover pills, anyway. I always wonder what the insurance situation is, but however un(der)-insured they may be, it has to be better than the alternative.