Pretty sure there is more to this story. So when you say Apple Care couldn't do anything for you did you have to pay for the repair?
Leaving aside any self-reporting, there are no user-creatable situations in which a battery will
ever swell up like that short of opening the machine up and damaging the charge controller or some other catastrophic damage like pouring water in it (and even that shouldn't cause battery swelling outside really weird cases).
If the MacBook seriously overheated, it could theoretically cause damage, but it would not result in that failure mode. So I'm fairly certain that Apple should and did pay for this repair, and it wasn't caused by the user.
And honestly, even if you did abusively overheat it (running it hard under a blanket or something), Apple would probably fix it assuming the failure was caused by something else. Really, the thing should thermally throttle to prevent damage anyway, so even thermal abuse shouldn't cause hardware failure, though it might increase the chance of premature chip failures.
Sometimes stuff just breaks. Usually older stuff, but once in a while newer stuff. Sucks when it happens, but it's a side effect of living in a material world rife with uncertainties. If
everything made by a particular company breaks, that's something to complain about. If the company refuses to fix something that is broken under warranty, that's something to complain about. If you're unlucky enough to be the one-in-1000 infant failure and it gets fixed without cost to you, that's just life.
Aside: I had a friend in high school who was running a Mac LC as a dial-up BBS server, and he put a comforter on top of it because the fan was loud. It actually worked that way for quite a while before it cooked itself to death.