Given a flat tire

We were given a car with a flat tire. Tire pressure light immediately came out 15 km after we left. We filled up the tire each morning for 3 days until it got really bad. Brought it to the Verona airport to exchange cars and they insisted the tire wasn’t flat. I told them I just filled it up 10 minutes ago so we could get there. They then charged us for another whole rental which cost more for 3 days than the original charge of a car for 7 days. I paid for two car rentals. I tried to have them think logically saying why would I drive out of the way while on vacation to exchange a car for the same thing or lesser if there wasn’t a problem. Sure enough as they argued you could see the tire got flat. They never even apologized. It was an extremely unpleasant experience