Almost certainly true, but I’m sure the knee-jerk reaction will be to claim that because this hospital almost certainly receives government money, it shouldn’t be able to decline to provide legally permissible services.
I should say that I’ve never felt this argument is nearly as iron-clad as its proponents believe. There’s no reason that in a secular, pluralistic democracy (as opposed to a theocracy, or an explicitly atheistic government) that this follows. The government (at least in theory) is neutral towards the rightness or wrongness of particular religious traditions and should be free to provide funding for a variety of institutions, with potentially contradictory elements, to serve a specific role so long as it serves the common good.
The government provides a hospitals money because they perform services which benefit society. While Catholic hospitals may not perform certain medical interventions (e.g., sterilization, abortion, euthanasia, etc.), the money that would have been spent on these interventions will doubtless be used in some other way. And so just as we find it perfectly acceptable for an orthopedic surgeon to limit his scope of practice to hip and knee replacements, or just as we find it acceptable for specialized clinics to possess a scope less than the full scope or practice, there’s no reason that this rationale can’t be applied to religious hospitals.
Besides, whatever surgery this particular hospital performs instead of this hysterectomy will free up another, non-Catholic hospital to perform the requested surgery.