Well, now you're moving the goalposts aren't you? Putting something up as collateral doesn't mean you don't own it, at least not to anyone I've ever talked to.
Do you also believe that if I'd bought the car (at a much higher interest rate) with an unsecured personal loan I'd also not own it?
And if you're going to talk about property seizure if you're severely delinquent on a debt, well none of us own anything... Just look at people who didn't pay their debt, went to court and were ordered to pay, and didn't - eventually the local sheriff can come and start auctioning off property to get that judgement paid.
So I don't really get your point. I own the car for any purpose I can imagine. Heck, I can even sell the car to someone else, and either they or I can pay off the loan. I've done this several times when trading in a car. Now, it'd be crazy for someone to pay me full value of the car without taking the lein into account, but that's really no different than taking expected maintenance or wear item replacement into account.
However, as far as I know, the purchaser doesn't have to do that, and can keep making payments or contract with me to keep making the payments, and as long as the lein is made good, it doesn't matter who owns the car.
It's like you can't wrap your head around buying debt obligations along with assets, but this is very common in many situations, and would also apply here.