I agree with Mr. S. I do check my tire pressure obsessively before just about every ride and keep those tires pumped. I don't mind getting dirty, either. I just am mechanically challenged. One of my proudest moments was when I was riding with Denise G. and she had a flat on her Friday. She could not get the tire back on the rim, no way. I took the tire from her and had it on in a second...

I laughed at that image of a little guy running behind a rider, ready to change a flat. I don't think it sounds so bad... I once read about a sort of Triple A for bikes, but don't remember the details.
I did have to call a taxi once, but there were 4 of us and it was a case of torrential rain and thunder/lightning and being 30 miles from our cars.