Just because the books declare you can do it, doesn't mean it isn't cheating. Cheating is more than simply "did you follow the rules?" If someone developed a device that allows you to read other people's minds, and secretly used it in order to win at a poker tournament, do you think that they would not be classified as "cheating" just because the rules don't explicitly say that telepathy is cheating?
This example does not match what I described. If a poker tournament's rules expressly state that telepathy is allowed, it can hardly be cheating to use a device to read other people's minds to win that tournament. Even though one might criticise the wisdom of the tournament organizers in formulating that rule.
Further, let's say you're in a chess tournament, and you learn only after that the waiver everyone has to sign actually included a deeply-buried clause saying that the referees may move any piece on the board to any location on the board that they could have reached by a valid sequence of moves. Would that not still be considered "cheating" by most people watching that tournament, even though technically speaking the rules specifically allowed for it?
Technically speaking, it would not be cheating. One could criticise my wisdom in joining a tournament without knowing all the rules.
"Cheating" is not simply "breaking an explicit rule". It is to participate dishonestly in some way. That's why we use it for related things, like breaking fidelity with one's significant other, or illicitly acquiring the answers to an exam in advance.
While cheating might not be simply breaking an explicit rule, it certainly isn't
following them!
The term for using a rule to gain illicit benefits by following it is "exploit"... but fudging, at least in the latest D&D text, isn't for the benefit of the DM. It's done only in service to players.
Given the book itself includes mention of not telling the players you do this, that would seem to be an admission that it is illicit--even if it is recommended by the book text, it is a violation of some kind, something worthy of the players' ire, should they discover it.
I don't take that meaning from the text. The text reads
you could ignore a Critical Hit to save a character’s life. Don’t alter die rolls too often, though, and never let the players know when you fudge a die roll.
On surface it doesn't offer a motive beyond "save a character's life". However it is a subsection "DM Die Rolling" in a section "Respect for the Players". The section is framed thusly
Your players need to know from the start that you’ll run a game that is fun, fair, and tailored for them; that you’ll allow each of them to contribute to the story; and that you’ll pay attention to them when they take their turns. Your players also count on you to make sure an adventure’s threats don’t target them personally. Never make players feel uncomfortable or threatened.
The placement and framing strongly imply that fudging will be done
out of respect for the players in order to let them contribute to the story, have fun, and enjoy a tailored experience in which they never feel uncomfortable or threatened. If you think those motives are better satisfied another way, then the rules offer an alternative
Rolling dice in the open demonstrates impartiality—you’re not fudging rolls to the characters’ benefit or detriment.
Although to my reading, the latest DMG leans more toward than against DM
partiality toward the players. They ought to be fans of the characters, collectively. I take the text as an expression of that along traditional lines; without agreeing that it is the best means to that ends. I don't impute unethical motives where there is evidence to the contrary... rather I take the design to be concerned for the player experience (with reasoning
@Enrahim has articulated.)