The answer to that one is quite simple - it is different because the roles of DM and Player are different. There's nothing at all strange about this. In games where a referee (or arbiter, or other figure concerned with meta-game issues) that role is typically wildly different from that of other players.
Why does the GM's role include fudging? I see the GM as the provider of the game world reality. Fudging to save a specific PC would make me wonder if they trust what they have created.
Conversely, a player has a vested personal interest in his PC. If anyone would have a reason for a specific PC to survive, it would be the player invested in them.
Perhaps it actually would make more sense if players were in charge of fudging to save their own PCs and GMs weren't.
On a thoroughly practical level, the DM should know far more about the context of the event and what is coming than the player does.
All the more reason not to subject the outcome to a GM's personal hesitancy. Such a decision carries with it an inherent bias, an imposition of the GM's preferences on the outcome. If a player cannot be trusted to fudge appropriately for their own PC, the GM certainly cannot be trusted to offer the players real freedom, as it is inevitible the GM's plans will clash with player choices, whether to a small or great extent.
I don't think it's wrong or awful for a parent to pick their child's college major. However, I don't think it's a good idea, either. I think giving the GM, with all their authority and tools and knowledge of the game, encouragement to fudge is much the same kind of problem. Good intentions are not in question. The question is the willingness to let things unfold as they will. Just as a parent, without any spirit of domination, might continue to nudge their offspring toward the "correct" college major, if they hold ultimate choice in their hands, a GM, without any disprespect toward his players, will certainly and definitely nudge the outcome of a game toward his or her ideal, and at that, the actual ideal, not the spoken one.
It is the dice that provide the GM an avenue to state truly, "This is your decision to make. You have a good estimation of the risks." Dice are democratic. They are also a blessing, a way of making possible what would be impossible: impartiality. Impartiality is the key that unlocks an imaginary reality in which choices matter. We already know that the imaginary world, being an invention of the GM, embodies his or her prejudices. The rules of the game transmute it into something apart from the personhood of the GM.
