It does not "shift" per se. If there is an accident involving a third party (e.g. the valet parker runs into another car), then that third party could sue any of the valet parking driver (as the potentially at-fault driver); the valet parking company (as his employer); or you (as the car's owner, who gave permission for someone else to drive your car--a car's owner is liable for the acts of permitted drivers).If the valet parket damages only your car through carelessness or intentionally, then in that case, you could sue either him or his employer for the damage.If the valet parker is not careless but some other driver runs into your car and is at fault in damaging it, you would sue that driver--the valet parker and his employer are not liable in the absence of fault.