I work for automakers' test and development programs. Most companies have a sign-out procedure that involves the keys kept in an automated kiosk that will not release them until you've done the paperwork and submitted a form, and your manager has clicked OK on the confirmation.

It's physically impossible to take the car without the system knowing who has it. If it has issues and you bring it back, guess what, you can't get the keys for the replacement until you've done the paperwork...

The fact that a company whose literal job is to keep track of cars, can't manage a similar level of rigor, blows my mind and smacks of negligence. If any harm befell these people beyond an hour's hassle and apologies all around, I wish them all success in the courts.

Some rental locations do something fairly similar. At the airports I've rented from, there's sort of a free-for-all on the floor itself, but then as you leave, your plate and paperwork are checked. Can't get over the severe-tire-damage strips until the system OKs you and the operator lowers the spikes. Why some locations lack a double-check, well, I suppose you'd have to ask them.