I think that it is odd that (at least to my perception), we seem to be talking just about a few things and ignoring others completely.
For example, we are continually bringing up protecting the PCs vs. letting them take their lumps. We are continually bringing up "trusting a DM" vs. being able to objectively verify their rolls.
I often roll dice behind a screen, and I fudge a LOT of them. However, I don't think I've ever fudged one to protect a PC, or to harm one (though that has often been a consequence). A lot of monsters have an attack that is once per encounter. That attack might even be their "signature attack" (say, the death gaze of a bodak). If I have one bodak in the encounter, and it misses with its one chance to use that attack, then no one in the party even gets to "see" what it does! I don't like encounters which don't actually feature the "special effects" of a monster. Sure, I could rewrite the monster so that the power was Reliable, but I can't see how that is any less of a "fudge" than a die roll would be.
On the flip side of the same coin, a monster might have a power which is really effective, and recharges only on a 6. If the monster sees exactly how effective it's big nasty attack is on turn 1, and can simply repeat it on turn 2 (when it rolls a 6), and then again in turn 3 (when I roll another 6), why in the world wouldn't it just do so? I don't see how deciding the monster is suddenly totally stupid is any less of a "fudge" than simply saying the power did not recharge. I'm not saying this is to protect the PCs. The power in question might simply immobilize them, or Stun them. What party wants to sit there through 3 turns doing nothing?
What I am arguing is that you can fudge to simply make a combat more varied and interesting, rather than just to adjust the difficulty level. If the big bad monster gets stunned in turn 1, and fails to save in turns 2, 3, 4, 5, and 6 (which is totally in the realms of possibility), then the party might have an easy, but uninteresting fight. Every group I have ever DMed would much rather have interesting than easy.
Yes, but by fudging, you are protecting or harming the PCs and dictating the results of the encounter by definition.
In this case, in the name of "interesting".
Some people justify their lack of DM impartiality in the name of fun, or the name of interesting, or the name of fairness, or in the name of the continuation of the campaign.
Also, I still don't see how "fudging the dice" is totally a matter of DM trust, but the DM altering the tactics of the monsters, or the composition of the encounter, to adjust for the players is not. If the monsters are supposedly existing in this "real fantasy world", then they should be the same whether the group has 4 strikers or a balanced party of 6, or a huge party of 12. How is it totally OK to adjust the entire world that the PCs encounter, based on the party makeup, and "cheating" to alter a roll occasionally?
It's one thing to create an interesting balanced encounter for the group that you have. Typically, the DM should limit this to number of PCs, but there is often a need to not introduce certain types of encounters if the PCs are lacking certain roles or abilities. It's hard to overcome flying monsters if nobody has a ranged attack.
It's something else to fudge the game on the fly in an attempt to make it more interesting.
Take your death gaze example. 5 PCs lose a healing surge because the DM decided that it would be cool

to force a PC to 0 hit points.
The thing I don't like about fudging is that DMs are not omniscient. When the DM is impartial (or at least tries to be impartial), then unexpected events can more likely occur such as 3 PCs out of 5 are unconscious. What do the other 2 do to save the day? That is a lot more interesting to me as a player than seeing a PC knocked to zero so that the DM could show off death gaze.
Opps, sorry. The DM didn't allow multiple PCs to go unconscious. So, the players are not in an interesting situation where they have to pull a miracle out of their butts.
Or alternatively, the PCs kick major butt and win in style without the DM slowing that down. For example, a few weeks back, our group killed the BBEG Lich in an n+4 encounter in 2 rounds and the rest of the encounter foes in 2 more rounds, it was a major encounter and the end of a major adventure and quest. On paper, it should have easily lasted 8 or more rounds (based on number of hit points to take out foes) and been seriously challenging, but it was done in 4 rounds due to luck (multiple crits) and tactics. That was fun and interesting for them, but it wouldn't happen in a fudged game. They walked out of that encounter high fiving. The DM might think "oh, all my hard work wasted". The players thought "what a great fight, we kicked some serious Lich tail".
By railroading the game with a lot of on the fly adjustments, the DM dictates more than just the scenario, he dictates the results of the scenario. Maybe without even realizing it. By making it harder (regardless of motive like making it interesting), he forces the PCs to use up more resources. By making it easier, he allows the PCs to use up fewer resources.
There is a difference between having a heavy influence on the creation of a scenario, and having a heavy influence on the results of a scenario.
By fudging, DMs insert themselves into the results of the scenario. They should only do that to the level at which the monsters have capabilities and intelligence. Not more, not less.