Taking the article as fact, if the nurse merely volunteered to pray for/ with the patient, and the patient said no, the nurse said OK, I personally don't see anything amiss.

News articles are often slanted and get certain facts wrong or leave facts out: What if in fact she mentioned this to the patient more than once, or prayed long and loud within the patient's hearing in spite of the patient's wishes.
On the other hand, the patient may indeed be sensitive and felt a need to report it.

I think the nurse went out on a bit of a limb here and should exercise her religious fortitude and realize that sometimes we're punished for our good deeds because there's a lot of people out there who don't see the world the way we do, and this was a possible, however unlikely outcome of her, for want of a better expression, sticking her neck out.