In the second encounter of "Let the truth be buried" can heroes use fatigues to move? It doesn't say they can, but it doesn't say they can't. It just states that when a hero performs a move action, he only receives 1 movement point , regardless of his speed or hero abilities.

I don't have the book, but in that case, I would say yes (the quest rules only affect move actions). Also, hero abilities that grant movement points that aren't part of move actions would technically still be allowed, though the inclusion of hero abilities in there might make it seem otherwise. They may only be referring to abilities (which may not even exist at the moment) that grant extra movement points to movement actions.

Otherwise, it seems that they would also say "Heroes may only receive movement points from move actions."

I would have to agree. A fatigue for movement is not a move action. This is how heroes can get around the OL playing Tripwire.

It doesn't say they can, but it doesn't say they can't.

Quest rules override normal rules when they contradict each other. That said, when they don't contradict each other, normal rules apply. If the quest says nothing about spending fatigue to move, then the heroes may spend to fatigue to move as usual.