I think maybe we are talking about different things. I took the op's post to mean he flat out moved the cb, as in moved it far. A slight rub, which I have seen many times, is fine. I thought that went without saying. If that was the case, then I agree, the thread should have ended. If the guy touched the cb and the cb went meandering off, I think it is a foul. People have to have more control than that.
Frozen balls just can't miraculously get put back where they were either. You know that. I can think of many instances where a player who was thinking could use this to their advantage, and suffer no penalty.
On the other subject you broached, that is actually very interesting. Has anybody ever noticed, in tournament play especially, that players who are not thinking in my opinion will handle balls when there is a possibility of a foul, yet they don't need to? They could have their opponent or ref do it. I have noticed this many times. You are right though in that if 2 players are thinking, why would they want to be the one to spot it. Anyway, I still think really moving the cb should technically be a foul
Whether you call it or not is up to the player.