I don't buy it. If their kid needed a couple thousand dollars to live, a lot more people would be able to scrounge it up. If they can't do the same for their pet, maybe they actually do love their pet less ... and that's OK.
While I agree that many (most) people would make it work if it were for a child, I wouldn't use the insanity of the US's human healthcare bills to justify anything. It's also insane and a travesty that you can walk into your hospital and walk out with multi-thousand dollar charges you cannot pay. Both can be terrible and unjustifiable.
On the other hand, your pet will die in your lifetime, unless you are very old or die unexpectedly. So most people are probably prepared for this emotionally on some level.