I think Discipline as the book has it is correct.
Its about trying to get someone to believe you, rather than what they already thought was the case. If they had no thoughts as to the matter in the first place, then I don't think you ought to be rolling for that. Its more of a personality thing, then. Trusting folks will just believe if they haven't heard otherwise. If they have no reason to disbelieve you, they're not opposing you. Skeptics might try to confirm or deny it with other sources. Belligerent people who don't like you will disbelieve you on principle, in which case Discipline makes sense again.
Think of Discipline here as mental Discipline, how well you keep up your mental barriers and ignore distractions, especially since a good lie is all about distracting people from the evidence that points out how you're wrong. It also makes sense in the sense of trusting in your dogma and training. In the Stormtrooper example, he would trust that unless the characters follow all the proper procedures to prove that they're secret agents or whatever, as laid out in Imperial Operations Manual such-and-such. If he fails his Discipline, he lets his personal judgement overcome his training and military discipline.
As far as the noticing facial ticks stuff, that's been proven to be BS in real life. It doesn't work, and the people who think they can spot a lie from that sort of stuff are more often wrong then people who have no training at all, unless you actually know that person really well and know their particular ticks. It doesn't work on Joe Shmoe you just met.
The only way to really tell if someone is lying is by asking more questions and looking for holes in their story, get them to trip up. This is also why Discipline is good, since it means keeping track of the details of their story and spotting the flaws, which good mental discipline would help with.