It's not like that at all.
Would you be willing to elaborate? Because, at least at the moment, I'm absolutely with JRRNeiklot and Hussar on this. I do not see how it's different; the umpire is an allegedly impartial figure officiating the game, and is required to determine particular disputed results. The DM is required to maintain a specific kind of impartiality, lest the game descend into "rocks fall, everyone dies" territory, and decides how to resolve proposed actions. I see fudging as the umpire declaring that a particular rule will be applied to resolve the dispute, while secretly thinking, "It will be better for the game if I decide X," regardless of what the related rule says.
The analogy seems very, very close. What problems do you have with it?
The 1e DMG tells you to understand the rules and then cut portions as needed to maintain excitement. Then it gives an example of ignoring a wandering monster roll that indicates a wandering monster on the fly as it comes up. That's not just changing the rules. That's Rulings Over Rules. 3e in the adjudicating section of the DMG says that the DM can supersede the rules, overturning them. That's not house ruling. That's Rulings Over Rules. 2e was no different.
The only difference between those editions and 5e is the packaging of Rulings Over Rules.
So...uh...what IS the difference between "house ruling" and "rulings over rules"? Because it sounds like the only difference is that house rules are consistent and defined, while "rulings over rules" is...neither. Yet you have specifically said that your application of fudging, which you classify as a "rulings over rules" situation, is both consistent and well-defined. (And I thought--but I could be mistaken--that you believed fudging was *not* an example of Rule 0 in action...?)