@mcc I don't see how this analogy could be helpful here; I also didn't get the impression that O'Dowd was trying to imply anything like that.
To me this is a completely ordinary rotation, it's just that some objects (spin n + .5 where n is integer) behave like that under rotation — this seems familiar when you've used quaternions for 3D graphics or similar.
Watching this could help: https://www.youtube.com/watch?v=pKKy2mmsziI