No. When you finance a car the lender gets a lien on the title. The title is still in your name. Usually one of the stipulations the lender places in their contact is that they hold the title for you in what is effectively "escrow" until the loan is paid off. Then they release the lien and send you your title.

The reason they do that is because a lien gives them the ability to, within a particular legal framework, get ownership of the car if you don't pay your loan, prevent the title from being transferred to someone they don't trust, etc. It's basically just risk mitigation.

That's what I thought too. I got pulled over once and the cop asked me "Is this your car?". I replied "Well, no... the bank owns it, but they let me drive it". He was not amused, but I was not being snarky -- I took the question to mean: "Do you own this car?", and the honest answer was no - at least, as I understood it, because the owner name on the title was the bank, not mine.

I assume the majority of people would understand the cop’s question as “Are you the person responsible and have the legal right to control this vehicle right now in this very moment”.

As others have noted, states typically have you on the title and the bank just has a lien, so I’m not sure that would even be technically accurate. And even if accurate, your tone is too lackadaisical and overclever for this kind of interaction. You could have said, “in the lay sense, yes, though the bank is the owner of record.”