"Whoops, I meant to put something like a kobold in this room -- but I can see now that when I was making my notes for this dungeon entrance, I accidentally wrote down half this stat block from the Bolrog stats. And darn, we've just rolled initiative. It'll slow the game down to grab the book and look things up. I'll just adjust things on the fly."
That's not a valid example of changing things on the fly - Typos aren't design choices.
To address most of the rest of your post, I will simply say that you seem to be claiming 100% accuracy at guessing whether or not your players will have fun with any particular outcome of a situation... and while that is sometimes obvious, there are those of us out here that want to see TPKs often enough that every time we survive through an adventure it feels like a true accomplishment - so you might misstep quite easily just by making an accidentally impossible encounter into an intentionally possible one.
In general, I feel that all the examples you make of times where you feel justified making on-the-fly adjustments are times where an adjustment should be made... but that adjustment can, and should, be made before
any in-play interaction with the elements has begun. The monster stats are wrong - you change it before the players even know there is a combat coming up, not once you can see how the combat is actually playing out.
And I'll invoke a little Gygax myself: "The game is the thing, and certain rules can be distorted or disregarded altogether in favor of play." (DMG, Revised Edition, 1979, page 9).
I agree with Gygax on that matter - so long as those distortions and disregardings are discussed with all players involved and decided upon as a group before play starts. In the case of those rare matters that can't be brought up and agreed upon before play, you halt the game the instant it comes up and publicly discuss the matter, take a quick vote and move on... because the guy behind the screen cannot be absolutely sure he knows what is best.
This comes in a discussion of rolling up a wandering monster as per the rules, but judging that result to perhaps be a detriment to the game, based on what is happening at that point in the campaign. These games don't run themselves; human input and judgment is vital.
The bolded portion is absolutely true, and is the exact premise upon which I have based my entire running style - and runs directly counter to the first portion.
There are no. such. thing.
as random monster encounters. Either the Judge wants that monster there and has intentionally placed it there, or there is no monster there at all... and that is how you perfectly handle the situation of "oh man, I rolled a flock of 6 Gorgons here but that would be too much for a wounded party to even remotely handle... I'd better ignore the dice"
I'm not advocating willy-nilly re-spinning of rules throughout a game. Last year, I came off a 3+ years GMing stint. I think I fudged rolls maybe five or six times during those campaigns. Perhaps not even that much.
Compared to the absolute zero times I have fudged rolls in the last 16 years, that seems very willy-nilly.
The bottom line is, everyone playing should have the maximum fun possible. If, in aiming squarely at that goal, I override a die roll to increase the enjoyment of the game for the maximum possible number of participants, I am playing correctly. And playing fairly, too.
This is where my bottom line differs - everyone playing should have the maximum fun possible. I cannot possible be certain of the exact maximum amount of enjoyment anyone can have, nor can I be absolutely certain of what will cause them that level of enjoyment.
So I must simply write the best campaign I can muster and see how the players like it.
As for playing "correctly" - no need to get defensive. I am not saying you are doing something incorrect with your practices... just that I see mine as more efficient (subjectively, of course) to the point that I do not understand yours.