Rivals events have different restrictions, which you can see by pressing X on the selection screen. Some of them have restrictions that tune must be stock. And ownership must be "Rented", which is just a way of enforcing that. The game gives you the car and tune that we are all running, even if you don't already own it, and we're all playing with the exact same setup. If it were just the stock tune requirements on an owned car, you might still have access to some things like tire pressure adjustments. But with Rented, you don't have access to that either. So that way it's the same for everybody.
I don't have the game open right now, so I can't check but I'm 98% certain it doesn't cost you anything to rent. I've got enough credits that I could be eating the cost and not noticing, but I don't think so.