I don't agree re trust, nor do I. Believe in false apologies. Will reply at length later.
ETA: I think there's not really much trust to break, although a rule was broken. In law school I was aware that cheating went on, and didn't trust people in general not to cheat. People act according to their lights. That's why even at schools that have honor codes, there are anti-cheating measures. Anti-cheating rules exist based on inherent agreements about fairness, but that doesn't mean that a child needs to apologize as if he's personally broken a trust with specific people-- and I don't really think that it's true to say that that's occurred here, either.
I don't think that much is gained by having a child recite an apology which doesn't come from the heart. The real reasons that people apologize when caught range from trying to increase the chance of clemency, to embarrassment, but rarely in a case like this (where, remember, the child doesn't seem to really understand or admit yet that he's actually done much wrong) to a full realization of the moral wrong and an empathetic feeling of the impact to others-- which really doesn't exist here at all, since cheating comes up fairly regularly in schooling children. (I also don't think shame is the best reason to apologize, although it can certainly be one motivation.) I'd wager that the school people involved are probably more worried about the impact to his personal growth than feeling wronged based on a breach of trust.
When a child is caught cheating and the parent forces her to apologize, the reasons for the parent doing this can include wanting to train a child in the right behavior (but this has the problems of the child giving an empty performance and perhaps learning that appearances are what matter, as well as not learning a deep appreciation for why the misconduct was really wrong), and the parent's own embarrassment. I don't think either of these is a good reason to force a child to "apologize".
Even if I had an AS child and believed as DeeDee does, that emotion follows action even or especially in AS people, I would work first on trying to help the child understand why cheating was wrong and not a good strategy in the long run, instead of forcing the child into some pat agreement that it was wrong.
Here, it's obvious that the child was trying to protect his own self-concept and/or that of others about him; there's no valid dispute over whether perfectionism is involved. In this case, what's happened is that the child acted out of weakness, likely already knows it was wrong on some level and may feel bad because of the moral aspects of it, and has been punished in a way that can be hardest to bear for someone with perfectionism: he's been proven to be imperfect not only in task performance but morally.
The OP's kid probably feels like everyone is viewing him as a total fraud and as possibly less intelligent than he's been made out to be. Shaming him further is really unnecessary and is just going to add to his heavy burden. The only way he should be forced to apologize is as extra punishment, but I don't think that's a good reason in this case.
