UPDATE
Thanks for the support and advice.
Anyone saying that Apple isn't obligated to fix anything wrong with an out of warranty computer, I don't disagree. Like I said, I wouldn't be upset if they decided not to replace a normal, somewhat expected problem due to aged hardware or normal to heavy use.
But a battery with 31 load cycles in just a little over a year swelling up and being told that it's normal... and on top of that, Apple just recalled however many batteries for the exact same symptoms just a while back, so I don't think it's unreasonable to expect good customer service. Anyone that does find that unreasonable is drinking the Kool-Aid.
Anyway, my mom made an appointment and took it into the Apple store, and they were kind enough to give her a replacement battery. Maybe they were more sympathetic than the AppleCare folks on the phone because they got to see just how swollen the battery actually was (it was fat, see pics).
So much thanks to the geniuses at Southpoint in Durham NC for making mom happy.