I think you're expressing far too rigid a position. The idea is to play the game and have fun. If things are going in a direction which the DM believes won't be fun for the players then doing nothing isn't serving the game well and it isn't a sign of good DMing.
Note the word "believes" in your argument.
You are assuming here that the DM is the final arbitrator of fun.
This is a re-occurring POV that has been espoused here on the boards and within the community for quite some time now.
What the players want to do and where the players want to go isn't as much fun as what the DM wants the players to do and where the DM wants the players to go. Another word for this is railroading (even if only done to a mild level).
Take a simple example.
The DM has an adventure set up in the hills next to the town. Orcs from the hills are sneaking down and stealing cattle.
The players hear that on the other side of the town is a swamp. The players decide to go to the swamp to find these cattle stealers.
The DM has 3 basic choices:
1) Interfere with the player decision and tell them "Nope, you are going the wrong way". (your basic choice). This could also be a more mild suggestion, but in either case, the DM is interfering with the player decision.
2) Let the players go to the swamp, but don't create anything interesting there for them to investigate (nobody's choice).
3) Let the players go to the swamp, but create a different interesting adventure there for them to investigate (my choice). They'll eventually get back to the hill adventure. Or not. (or the DM could just introduce clues in the swamp that will eventually lead back to the hill adventure).
Sure, if the only choice is between #1 and #2, then yes. The DM will know that #1 is more fun than #2.
But if the choice is between #1 and #3, then no, the DM does not know that #1 is more fun than #3 unless he creates a fairly subpar adventure #3. And even then, the players might think that the swamp adventure was as much or more fun than the hill adventure, even if the DM doesn't think that.
This is a simple example, but it illustrates the point. This gaming community concept that that DM knows more about what is fun or not for everyone without even attempting to allow the players to make their own decisions and reacting to those decisions is in error from my POV.
Let the players play.
Let them make mistakes.
Don't make decisions for them.
The game can be just as much fun or more fun doing that then to be their wetnurse.
No doubt. This is an interactive game where the DM is there as well and even minor statements by the DM will be strongly considered by the players.
But, the role of the DM is not the role of the player. He should not be making party decisions and directly influencing the group. He will be presenting information and indirectly (and for some people, directly) influencing the group already because that is part of his role. But as a general rule, he should not cross the line into being the equivalent of a strong influential party member or PC. He has too much influence at the table already and giving him more, as per your vernacular, "isn't a sign of good DMing". Obviously, IMO, YMMV.
I cannot tell you the number of times that I've seen in a game where it went something like:
Player 1: "I think we should go down to the markeplace late tonight and try to sneak into that building."
DM: "The building will have heavy guards." (not that this was mentioned before, the DM is throwing out something new that the players may or may not have known or thought of previously, just because the DM is omnipotent for his world)
Player 2: "Let's not do that. Those guards were tough last time and we don't want to get into a fight."
What a way to shut down a good potential adventure Mr. DM. There is nothing wrong with Player 2 coming up with the idea to not do so because of the guards, but it's problematic when the DM throws in his 2 cents and throws the game into a totally different direction. He's not playing a PC. He shouldn't be "nudging".