It's actually is one of the rare instances I've seen "do a 360" used appropriately. Facebook revamped their policy around the issue while ending up at exactly the same place: you have to use your real name.
But doing a 360 doesn't mean doing a 180, and then sometime much later, doing another 180.
I think it's a matter of context and time-frame. If the end up pointing the same way they started, that's 360 degrees. That might entail two 180 flips at different points, and if talking about one of those specifically, it would be appropriate to say they did a 180 when referring to that specific situation.