Apparently, St. Joe's was not complying with the Diocese's other pro-life directives, so as head of the Phoenix Diocese, Bishop Olmstead was perfectly within his rights to do this. The hospital is still in business, just not as a Catholic facility. This was obviously their decision as they refused to submit to the Church's authority.
BTW, Catholic Healthcare West is headed by an avowed Obama supporter, Lloyd Dean. He's also black, gave Obama about a 100 grand during the campaign, was an enthusiastic backer of Obamacare, and isn't even Catholic. That whole chain is Catholic in name only, IMO.
Mrs. Prince of Space
However: If the baby would die either way (either in his mother's womb, or outside of it), simply to move him (gently, without further harm) from inside his mothers body to outside, would be neutral with respect to his survivability. So in a very small number of extreme cases, the intact, live delivery of the pre-viable child can be morally permitted if the intent is not to harm the child.
In other words, in the womb, he is doomed to die; delivered prematurely, he is still doomed to die (no real change in life expectancy, which is slight in either case) but, live and intact, the dying child could still benefit in real ways: the child could be held and loved by his mother and father, even if very briefly; the child could even be baptized; and the mother can survive.
This seems to be the position taken by Germain Grisez, an eminent and very pro-life Catholic moral theologian, here: http://tinyurl.com/not-to-shorten-babys-life.
Delivering a baby very prematurely but intact and alive is not, then, an intrinsic moral evil: because in the above case his life expectancy is unaffected (since death is imminent in either case), and he can derive benefit from being alive outside the womb.
This would not be the case if the baby was killed and removed by a D&C or a D&E. This is what the Diocese of Phoenix implied happened: see http://tinyurl.com/Diocese-of-Phoenix-Q-A.
Obviously if you dismember the baby, you are directly intending his death, and this is murder.
Dr. William Chavira, a pro-life physician and member of the Diocesan medical ethics board, apparently thinks it would have been morally permissible for them to induce labor in a way that didn't directly kill the child. See the highlighted section Here (Link).
Putting it all together, it looks like the Bishop and the Catholic ethics people would not have objected, in extremis, if further delays would be fatal, and after all other options proved futile, had they delivered the baby alive, even if it were to perish within minutes. What they objected to was the direct slaying of the child by dismemberment.
The intact delivery would have been treating the baby respectfully as a dying person, and would have saved the mother. Abortion-by-Dismemberment is treating him like butchered meat.