I think that a healer could fix the dislocated shoulder they just have to be a higher level and the reason we've only seen people turned away is cause so far most healers are biased against the poor dudes and only want rich patients so the better healers don't heal them.
RIGHT? the dude recommending to burn the town to get rid of rats is crazy.. but it's part of the story, i guess it's to show that the nobles are THAT ignorant
But I wonder how people get to rely on heal so much if can't even fix a dislocated shoulder