Yes they would. They would have to be lying about whether their motives are the same as those of hundreds of thousands of people who actually implemented their policy, and of the tens of millions who supported it politically.

I think you meant to respond at this thread. You're moving the goal posts. The question isn't whether "the government" (i.e., some conspiratorial subset of the entire government) have the same motives as the superset which implements their purposes (at least not according to the characteristics of a "Conspiracy Theory" you specified). The question is whether "the government" has to hold secret, ulterior motives that differ from their acknowledged, public motives. I see no reason why any conspiracy theory about 9/11 requires this. You might very well argue that they require a different belief about which actions will best secure the goals implied by the motives--but that is a completely different question. (E.g., Marxists and the Austrian School both claim that their motives are foster a stable, sustainable, healthy society--but they have radically different ideas about how to achieve this goal).

That's false.

It may be false, but that doesn't prevent it from being a motivating factor for those who believe it is true.