Is it possible they don't ever intend to exit? I know that's pretty rare- most startups seem to be aiming for the exit- but can't some simply be trying to be their own business?

Why is it so rare? If I had the choice between being the owner of and working at a company that I love and believe in while earning $x, versus earning $10x, the former sounds much more attractive.

Sure, I suppose it is...it's just rare.

6 Billion is a lot of money to turn down, but I've never been in their shoes, so I can't say what I'd do.