I've read the NYT article and I'm left in the situation of attempting to look at this matter through the eyes of American law.
Here, the situation would be cut and dried.
Health workers have a right to ask not to be assigned to certain types of cases. Abortion for example. (But as far as I know, not attempting suicide, strange that one). However, that request is simply a request. All patients must be treated according to professional standards, not religious convictions. If that isn't acceptable, then don't take the pay and don't do the job. Our system here is essentially one of intent. Intent of Parliament. Intent of the individual.
In the US, your legal system seems based argument. The original intent seems irrelevant. If a comma is misplaced or a word misspelt, or there exists as previous reference, that can affect the judgement so far as to create a different law.
This woman would be completely wrong here, simply because she has allowed her personal convictions to be superior to her professional ethics.
In America, no doubt, the case will rest upon some nuance or some wording detail.
