Well let's put some nuance in the situation.
Honestly, there's not much nuance for me. If you decide to use a game's random outcome-determination method, but after seeing the result you decide to change it, that's where my line is. I don't do it, and I don't want to play in a game where it's done.
If you don't want to abide by a random roll, don't roll. Or make the roll with different parameters. It's that simple.
As far as I'm concerned many of the other things you describe, or that have been described upthread, are exactly what I use as
alternatives to altering the die roll. IMO and IME, altering the die roll (or rolling in secret, which leads to the players assuming you're altering die rolls) leads to the players believing that the DM is going soft on them or to the players believing that the DM is adversarial. IMO and IME, neither one of those is fun or good for an RPG.
This is where Raven Crowking and Ariosto and I part ways (I think). Because I don't have any problem, as DM or as player, with a DM altering an encounter -- in effect, changing the rules, which from then on will be adhered to -- because the DM screwed up in designing or vetting an encounter. (Similarly, I don't have a problem with a DM "winging" an encounter or an entire adventure. Well, except that it's
usually inferior to a prepared adventure.)
By contrast, I will not alter a fair encounter (not necessarily "evenly matched," because "fair" and evenly matched" aren't always the same thing) that turns out differently than I might have expected because of player choice and/or dice rolls. And I do not want a DM doing that when I'm a player.
Again, really not much nuance. It comes down to this, for me:
"If you've decided that something should be determined randomly,
stick with it. If you're not going to stick with what you roll, then why the hell are you pretending you want things determined randomly? Just declare the outcome and be honest with yourself and your players." (Which, not to belabor the point, is exactly what M&M has built into the system.)