No you don't...any required repairs is the responsibility of uHaul unless it's physical damage that you caused, ie you smash a piece of their equipment into something immovable. Mechanical issues (including tire failure) is not your fault however. I once watched them perform about about $2000 worth of repairs (before the tickets lol) in the scale in Oakville on a junker they rented me. That's another story.
That's not exactly reliable though....like the time the (maybe 17 year old) girl working at the north oshawa store tried to tell me that my 3500 Diesel 1 ton dually wasn't rated to pull their 8x10 enclosed. I showed her a picture of it on my phone pulling our 35' Fifth wheel with our jetski trailer (and 2 skis on it) behind the fifth wheel and she still said "but the computer says I can't rent it to you". She didn't know what "dually" meant either. Eventually a guy from the back came and talked some common sense into her.