Nope, the act of lending is one form of a "transfer of the right of possession". And while the act of stealing does not include an explicit "transfer of the right of possession", it results in a "adverse possession".
The company purchasing the vehicle becomes the registered owner and has both possession and right of possession. The financial organization providing financing would become the lienholder and have a security interest that, upon default, would ripen into a right of retention (ius retentionis). If the business that bought the vehicle then rented it to someone, that individual would then have possession but would not have right of possession.
I purchase a pen at a store. I have all three attributes (possession, right of possession and right of property). If I loan the pen to someone, they have only possession.