You wrote:
“If the article is mistaken, what is the Catholic church’s relationship to the hospital and those who practice there?”
1) The Catholic Church doesn’t own the hospital. The church doesn’t pay the salary of anyone in the hospital either - except perhaps of the chaplain.
2) The Catholic Church doesn’t have the legal authority to hire or fire anyone in the hospital other than the Catholic chaplain.
3) The Catholic Church has spiritual authority over all the Catholics in the hospital. That means the bishop of the diocese can excommunicate Catholics there if they violate canon law. That is his decision, however, and realistically there is essentially no way to go over his head in the situation. Thus, as an institution, in real terms, the hospital is not under the control of the bishop and the Church.
And this proves my point in spades: http://www.sentinel.org/node/10753