Oh yes, that's definitely true, I can't believe I forgot that. Obviously it's not just about inflicting physical or sexual pain, but also psychological (with or without the physical/sexual element)... I don't know whether the definition of a punchbag fic should include the type of character typically featured in such fic, that seems like it could end up being horribly circular if we're trying to establish what kinds if characters get such treatment.
H/c seems to be a very common feature of such fics, but certainly not a required one...

Another common thread I've noticed is that the hurt element is typically inflicted by an outside force, such as an OC or a group of OCs (like the French soldiers in the fic that sparked all this debate) or a character who is a notable canon villain, rarely by a character who is thought to be a friend or ally (unless the fic is shamelessly and wilfully OOC). This could be because one of the key draws of such fics is the simplicity of their morality- punchbag fics typically have a clear moral divide between the hero/victim and the villain(s), as well as any potential rescuer/comfort giver. Whether this is a necessary and fundamental aspect of all punchbag fics I'm not sure yet but it seems very common to me.