I no longer use the Grooming Service, OR Banfield Medical Vet Services at Pet Smart.
Though I still go there for various items, I NEVER let my guys down on the floor for any reason. I put them in a Shopping Cart, and tie them in with their Leash's. Not so tight where they can't move around, just where they can't jump out, or get their feet/heads far enough out for another Dog to attack them.
I admit I am absolutely and profoundly paranoid about things like this, and take some rather extreme precautions about their protection.
It's a lot easier just to say no, than it is to go through the misery that causes one to write a Check out to a Vet Hospital or Burial Service.
Your can't, and no one will blame you for, being too careful.