Why bother?

Please read this story:

http://www.foxnews.com/story/0,2933,164546,00.html

It's quite sad, really. My question leaving this article is this: why did this woman's family, who chose to utilise all available medical care to keep their baby alive in dire and dangerous circumstances, even bother?
An even better question is: why did the doctors and the hospital do so? Is it not a medical establishment who would be possibly legally liable if they refused to murder a baby (oops, I mean, "perform an abortion") for a woman who requested such a crime (dang it! I mean, "procedure")?

For the latter question, I can only presume that not all medical establishments are identical - some voluntarily take in the abortuary side of business and some find it repulsive. As for the family, obviously they are Roman Catholic and so would not want to murder their child (not always a necessary connection, but we'll let it go for now).
But it really speaks volumes when we comprehend that it was totally up to the family whether the baby lived or died, and the state would have done nothing to punish them had they chosen differently.