I think you are both right. An ultimatum can be a demand for someone to stop destructive behavior, but it's more often a demand to fall in line, with the idea that you are replaceable if you don't.

I think the latter is what OP referenced, if someone is telling you "it's my way or the highway" and they are OK with the highway option, you should listen. They are telling you exactly how much you are valued (or not), as well communicating that they feel they are in no uncertain terms above you.