When is a purchase a purchase?

I recently read a thread on another forum I thought was interesting. It’s seems this guys orders a fifth wheel, it comes in, a PDI is performed and as normal, some items needed fixing. As the story unfolds he gets a loan, signs all the paperwork and leaves the dealership. Awaiting the Coach to be shipped to him once the PDI items are done. Now two weeks have passed and some things on the PDI list are not completed due to things needed from the manufacturer. He hopes to get the Coach next week but wonders if things would have worked better if he hadn’t already signed the paperwork?

After reading this I wondered when in fact is the Coach his? A friend of mine was a GM for a Cadillac dealer. He said he owns the car until it’s driven off the lot. The guy above didn’t say anything about not wanting the Coach. But when is the Coach actually his? When he signed the papers or when he takes delivery?