I actually didn't think that part belonged in there. Considering a rotating point of view seemed contrived to me.
You’re right, it’s contrived. But I automatically tried to compare lengths too. So it’s a good lesson in making sure that your simplification of the question still does what the question asks.
(Specifically, my "aha" was that one rotation of the moving coin in place was not the same as one rotation of the moving coin around the middle coin.)