In the example to start the thread, I mentioned that Player 1 basically asked to skip ahead to the dig, but it in no way was a demand. It wasn't a, "I'm not doing anything other than addressing the dig site, and any attempts to take me elsewhere will be met with opposition and 'shirtyness.'"

But I think a smart GM would pay attention to the clues leading up to that moment and divert it. "Hmmm, Player 1, sounds like you're having problems with the current courses of action on the table. What's happening? What are you looking for?" Get an answer, then take a 15-minute pit stop break and let the GM sort it out.
If I as a GM had information planned in the scene that was crucial to future progress, I'd either figure out a way to integrate it into a new, more player-engaged scene, or I'd say, "Listen, I know you're anxious to keep moving forward with X. But I want to let you know that there's several things here that I think will be relevant to your goals, once you understand them. Let me set up this scene for you, and see what you think. If you're REALLY not interested in it, then we'll ask the group to see if they'd like to move on as well." Then if what's presented doesn't seem to warrant player buy-in, the group decides to move on.
That takes a lot of maturity from both GM and players to get to that point, though. The GM has to not be hurt, or insulted, or whatever, that his players didn't want to engage with his or her carefully crafted "scene in the desert." I think, @
Hussar , your ultimate point is that a GM who is unwilling to take that approach is probably not going to be effective over the long-term, and I think I agree with you.