Backwoodsman, on the face of it, I'd agree that surely it's more polite to ask someone's permission than to pray "behind their back"

But having thought about it, actually I think that prayer is ultimately between the person praying and the deity they pray to. By asking someone else whether they would like to be "prayed for", you are implicitly telling them something of your own beliefs, and asking for approval. And a vulnerable patient might well feel a refusal would make things awkward. The same might happen if someone were to talk about their political views. That doesn't constitute a sackable offence, but I'd expect a healthcare professional to be a bit more sensitive in that respect.

Anyway, if I find myself in the same situation I shall answer "Yes, you can pray for me if it's helpful to you"