Interesting. The advice we get from our corporate travel agent is to never modify or try to fix a rental car. Always call for their repair service, no matter what the issue is - even if you think you can do it yourself. I had a flat tire one time and a blown fuse in the windshield wiper one time. (Both happened to be Hertz.) Both times I called the toll-free number on the rental agreement. A tow truck was sent to fix the flat - middle of nowhere Missouri - and the RAC (similar to AAA/CAA) was sent to fix the windshield fuse, which was thankfully at one of those really nice service areas on the British motorways.

No charge for either one... Unless I was offroading or otherwise driving dangerously, I'd be a little peeved about getting charged for a flat tire.