You have spoken of a GM telling players they don't ever fudge, but then going ahead and doing it anyway. That sounds like a pretty fundamental and active lie, to me, and a misrepresentation of the GM's basic GMing style. If you tell players that when they join your campaign, then yes, your gaming relationship with them is founded on a lie, one that is rather serious to some players.
I thought I was fairly clear - I am merely noting what I know of human psychology. Some small fibs are generally acceptable (even required, from a social standpoint), but others aren't. Humans aren't an "all or nothing" creature. We have subtleties.
I know that's what you are trying to do. But you will not convince them of that when your argument is, "It is okay to tell people the rule is X, but then you play with rule Y" (tell them you don't fudge, but go ahead and do it). That's going to come across as the very essence of cheating, no matter what the rulebooks say.
Meanwhile, my approach makes occasional fudging one of the rules, so I am not cheating.
Any uncertainty will continue to raise the question. A denial just works best in this case.