That's not entirely true. People in the middle ages ascribed all sorts of mystical magical abilities to saints and their relics. Having priests be able to do something with relics and pray to saints or gods for divine intervention seems entirely in keeping with what might have been expected in the RL middle ages (obviously, flashy things are mostly out, most things should probably be plausibly deniable as actual divine intervention, no matter what the priests claim).
They ascribed all kinds of things. People still do. Doesn't mean they were actually able to
do those things.
So, again: The only powers priests in BM are going to have are powers of influence. Not "divine intervention" or anything that's likely to look like it.
