Just guessing here:
I'm thinking the airline pays. They have to account for a number of situations that would require diversions, including mechanicals. I'm sure this is all accounted for, just like the gasoline they may have to dump in such cases. I read these days some info on dumping fuel and BA said it was only approximately 0.5% (IIRC) of their fuel that got dumped - hardly a significant figure. I'm sure the emergency situations that require diversions are rare enough and that airlines to account for that in their books (by adjusting the prices accordingly). Trying to bill a pax for an emergency landing can be really, really bad PR.