"I know people who swear they can change a rear tube and be re-inflated in 4 minutes."

And they can! When I was on a group bike trip in northern Minnesota everybody got lots of flats (due to riding on Hwy 169, which suffers from too many drunken Rangers tossing beer bottles out the windows of their pickup trucks). I repaired most of them myself, but every now and again one of those Spandex-clad super-bikers would stop to help, and they really DID have the whole thing done in less than 5 minutes. I was unable to get the tire on or off without tire levers, but these guys just peeled the tire off in seconds with their frighteningly muscular fingers.