This explanation is not totally convincing. The main issue is the OP actually just referred to very few scenes, while there is no proof that throughout all scenes this difference remained consistent. A more plausible explanation would be Nolan initially intended to use such a mechanism, but later decided to leave it out. However, since some of the scenes of the movie were already filmed, the ring could not be changed. It's obvious that Nolan put the spinning scene because he deliberately wanted to leave an equivocate ending. It's possible that in the beginning that wasn't his idea, and he changed it halfway through the movie. But what's clear is the ending was intended to be equivocate. He would not let such a vague "ring" mechanism co-exist with the spinning scene. That's far too strenuous.