The Animated Feature - SILVER
Before reading other answers -
I'm a bit confused at the situation. Why does Nathan assert that Alan can't attack with Mutavault? My assumption for the rest of my answer is that Nathan believes the game has already progressed to the Declare Attackers step, and it is thus too late to animate Mutavault.
Since this appears to be a communication problem, the first step is to investigate how they've been communicating in previous games. Since the scenario doesn't state any deviations, I assume they've been sticking to common shortcuts.
“Move to Combat” is already a defined tournament shortcut, meaning, “I'll pass priority until we enter the beginning of the combat phase”. Nathan says “Sure”, and the game moves to beginning of combat. Alan's tapping of the swamp, and attacking with the Mutavault, are basically an undeclared shortcut for “Activate Mutavault's ability, pass priority until it resolves, pass priority until we move to declare attackers, and declare Nightveil and Mutavault as attackers”. This is a legal sequence of plays.
If Nathan wants to interrupt this shortcut at any point (perhaps playing another Glimpse), he can do so. Otherwise, the line of play stands. There's no infraction, and no penalty.
After reading other answers -
I had to reread the scenario a few times, and then reread the MTR, to figure out why my answer disagreed. The MTR states that shortcuts like “ready for combat” or “move to attacks” offer to pass priority until the opponent has priority in the beginning of combat step. i.e., the player wants to move to declare attackers.
This is a bit surprising to me, since I would expect the phrase “move to combat” to mean that the player wants to pass to move into combat, and end up with priority in the Beginning of Combat step. Outside of timing/baiting trickery, this sequence of communication is how I usually see Mutavault handled by players. They offer to move into combat, then activate Mutavault, then attack.
That said, given the rest of the scenario, I think Alan expected we were right before the declare attackers step, when an opponent would normally cast pre-attacking tricks. When Nathan says “Sure” and the game moves to declare attackers, the sequence of activating mutavault and attacking with mutavault and spectre is illegal. In this case, it's a GE-GRV for Alan, with a warning, and the game rewinds to the beginning of declare attackers. Untap Spectre, Mutavault, and Swamp. Alan has the choice of whether to attack with Spectre or not.
This scenario is pretty interesting. Without the wrinkle about trying to bait out Glimpse the Sun God, the scenario seems to be how most attacks with Mutavault get played out. This may mean that most players are playing the card and related shortcuts incorrectly, and we might get some angle-shooting players in the future trying to enforce this. I think that, without the wrinkle of waiting for a combat trick, I would probably rule this as a legal line of play, with communication problems, and educate the players about the correct use of tournament shortcuts, communication, and the turn structure.