If someone is grievously injured, I think most people even remotely skilled at healing things would go so far as to cut them out of the clothing in order to wash and bind them. In any case, if their clothing is still perfectly intact and that difficult to remove, how deathly wounded can they really be? Probably most people in urgent need to hide themselves will flee from those trying to heal them, even in life or death situations, in order to prevent their identities from being known. Either that, or acknowledge that they're going to find out and it's worth it.(Edit - Too slow)