I never even came close to stating that "the people we trust are always right". You appear to be viewing the word "trust" entirely too much as a binary state. Tabooing that word for now...
Since we can't always spend the time and effort to verify a claim, it's important for people (and thus important to teach children) to be able to quickly assign a probability to the likelihood that a person is correct when they say something. There are a number of factors that can go into such a calculation, and they will differ based on the statement and the speaker. A person who has a known history of trying to deceive others should be assigned a lower prior probability of correctness than a person who has not shown such a history. A person who makes a large number of honest mistakes should also be assigned a lower probability than somebody who doesn't. However, that is where the similarities end.
An ardent young-earth creationist's views on geology should probably be assigned a very low prior probability of correctness, but if that same Y.E.C. has a PhD in economics, their views on something like inflation should probably be given a higher probability of correctness than those of most people. When you know the speaker has a tendency towards non-malicious incorrectness in a given area, you can use that information to discount their beliefs in that area without writing off everything the person says in all areas. You should still be skeptical of anything they say that seems unlikely, and you should expend the effort on verifying the claim that is appropriate to your live and the value of your time and effort given the probability that they are correct (taking into account things like how well peer-reviewed the position is, whether it contradicts common sense, etc., but also considering how well the person can be expected to know the field and whether they have any known reason to deceive people about it). All else being equal, there's no reason I know of to have a greater expectation that a Y.E.C. is incorrect about inflation than somebody who is not a Y.E.C.
For a person who has a known history of intentional deceit, it makes sense to use a lower prior probability of correctness for everything they say. A politician's promises are an excellent example; without going into any actual political side, I think we can all agree that politicians are far more likely to make false promises and deceptive claims than the average person who is not in (or striving for) a similar position of popular authority. There is reason to assign a lower prior probability of correctness to almost anything a politician says (publicly) than there is for an otherwise-equal non-politician.
Now step back from the broad categories of things like Y.E.C.s and politicians, and consider the people around you in your daily life. Most of them will have no motive to intentionally deceive you, but some will. Many of them will have biases towards incorrect positions in a lot of areas, but it would be inefficient (and socially awkward) to act as though a friend who has a known bias about a sports team as though they're a pathological liar about non-sports-things just because they're completely blind to that team's quality and you've caught them in a number of false claims about the team that they should have known were false. On the other hand, some people just are unreliable about things, or think it's funny to convince people of lies for no purpose but their own amusement, or have developed a reason to want to hurt you personally and will say whatever they think will have that effect. It is important to be able to tell the difference between those people and those who merely sometimes make honest mistakes.
Related: The Santa deception Is Santa real On the care of young rationalists
All of the other takes on this topic start from a point, when a child (usually 5-9 years old) asks "Is Santa real?" Nobody yet asked "how to raise my child Santa-free?" What to say, when a two-year-old, who just noticed that there is this character on TV asks "will he come to me, too?" A toddler may not yet understand the concept of lie, of pretending, of things not physically existing. How to tell her, what will happen, what to expect, how and why other children behave differently?
My three-year-old daughter discovered Santa last spring, which finally forced me to think: how to deal with it? Ignoring the thing worked for three years, but what now? I live in an extremely catholic country (Poland), so I cannot be completely blunt about it.
In the end I decided to call it "the fairy-tale of [Santa] Claus." For me it has a lot of advantages: this is a story that can be told, retold, reinvented and everybody knows it. In addition, since the name includes the phrase "the fairy-tale", it has just as much validity as the tale of the Red Riding Hood or any TV character that she likes.
I tested some of her beliefs about "Miko". I opened the box with books intended for gifts in front of her. When she wanted to read some of them, I explained that she cannot yet read her book, because she'll get it on Christmas Eve. She asked "is it from Miko?" and I replied that in some way it is, but I bought it. She didn't insist on reading it right now. A few days ago she helped me wrap some of the gifts. She commented that action "Miko brought these so we can wrap them and give them as gifts from Miko."
Malcolm told me, that he likes best the strategy, when you say that Santa Claus is a game that everyone plays. People pretend that there's a big guy in a suit who does the thing, and if you ever let down the pretense to your friends, you lose the game. I'm not entirely convinced by this strategy - it may be too complicated for a 2- or 3-year old (since my daughter didn't wrap her mind around the information that I bought the books).
What are other strategies that you use? Or which ones you don't like? Why?