The controversy here seems to stem from an premise that is baffling me right now: the idea that “cheat” implies “getting away with something”.
I don’t think it implies that at all, and have never understood it to do so. After all, people get “caught cheating” all the time, and don’t get away with doing it. In fact, getting “caught cheating” in other areas (relationships, athletics, academics, etc) often has rather severe repercussions.
Basically, to “cheat” on a diet means “not follow the rules” (like in anything else), or even to betray an agreement or relationship. To put it another way, if you are “faithful” to your diet, you don’t cheat on it, just like if you are faithful to a spouse.
But, people are willing to talk more freely about cheating on a diet because they understand it’s simply more acceptable to do/ there aren’t typically large moral issues with this specific set of actions (outside of particular circumstances). Some even argue there are benefits. The accuracy of that claim isn’t terribly important for simply understanding how that kind of understanding influences usage of the term as a whole, which is to say, it is casually used and admitted with typically less concern or sham than admitting to cheating in other matters.