You don't think the DMG saying that the GM controls EVERYTHING--that NOTHING is out of his control is enough?
It's got to actually say, "S'mon, a DM cannot cheat"?
Yes. The two are completely different. Elf Witch gave some great examples.
I don't generally find 'cheating' a particularly useful concept when it comes to GMing, and IME it is generally not a concept the rule books address at all, so there's no point you appealing to the rule books. They don't say "GMs can't cheat!" and they don't say "Don't cheat, GM!" either.
But there are certainly sorts of GMing that most players (and other GMs) would regard as cheating. For instance, fudging is not the same as cheating. Players may not like fudging, but fudging is not necessarily perceived as cheating.
Fudging dice rolls, monster hp, etc to create an entertaining story or to preserve PCs in an unexpectedly, unfairly overpowering encounter may or may not be seen as good GMing, but is not normally regarded as cheating. From what you've said, this is the kind of fudging you engage in.
Fudging dice rolls, monster hp etc to preserve a favoured GMPC in whose welfare the GM is personally invested, or to preserve a particular favoured PC at the expense of the other PCs, will often be seen as cheating, as Elf Witch says. Doing this to railroad PCs down a certain track may be seen as cheating too.
Whether GM behaviour is regarded as cheating or not is partly dependent on agreed norms, the table contract, which are partly derived from the books. The Conan RPG expects heavier scene/story framing than does OD&D. It seems ok in Conan to follow Conan story structure and plonk down PCs
in media res. How the story resolves is up to the players, but Fate Points are there to make PC death unlikely. In Vampire: The Masquerade and some other '90s games, a high degree of railroading seems to be acceptable - eg there may be canon NPCs who can't be killed, and this may be accepted by the players. They may still be annoyed if a PC-level GMPC adventuring with the PCs turns out to be invulnerable, invincible, gets all the best stuff, etc, or if one PC is blatantly favoured, and see the GM's fudging to ensure that as cheating.