I've had my car in a few times for service at the mothership, Fremont, and I have never been able to get a Tesla loaner. When they run out, they have a nearby Enterprise car rental which provides the loaner. It's free, but I have to fill out the Enterprise paperwork, and decline the extra insurance that they (fairly gently) push. Of course, I pay for the gas. It is similar to when I have my Lexus serviced at the dealer. I will sometimes get a Lexus loaner (though a cheaper model, never an LS460 like my car) but if they are out, then I get an Enterprise loaner.
Given the vagaries of service appointments (say a car takes an extra day - so the loaner which is expected back on Tuesday doesn't show up until Wednesday, or an owner comes back very late in the day to pick up his/her car and has the loaner for several hours longer than expected) I think the best they can do is first come first served until they run out of Tesla loaners. It would be nice for them to pick up the gas bill, or at least pay for the returning fill up. The way Enterprise works, you often don't get a full tank of gas, and are expected to return with the same amount as you had when you started.