The intelligent people are still humans, and can default to their intuition just like we can if they think that using unfiltered intuition would be the most accurate.

But by hypothesis, we are talking about a scenario where the intelligent person is proposing something that violently clashes with an intuition that is supposed to be common to everyone. So we're not talking about whether the intelligent person has an advantage in all situations, on average; we're talking about whether the intelligent person has an advantage, on average, in that particular class of situations.

In other words, we're talking about a situation where something has obviously gone wrong; the question is which is more likely to have gone wrong, the intuitions or the intelligent person. It doesn't seem to me that your argument addresses that question.

if the claim "the amount of computation that went into their opinions will be orders of magnitude smaller than the amount of computation that went into our intuitions" actually implied that intuitions were orders of magnitude better

That's not what it implies; or at least, that's not what I'm arguing it implies. I'm only arguing that it implies that, if we already know that something has gone wrong, if we have an obvious conflict between the intelligent person and the intuitions built up over the evolution of humans in general, it's more likely that the intelligent person's arguments have some mistake in them.

Also, there seems to be a bit of confusion about how the word "intuition" is being used. I'm not using it, and I don't think the OP was using it, just to refer to "unexamined beliefs" or something like that. I'm using it to refer speciflcally to beliefs like "mass murder is wrong", which have obvious reasonable grounds.

Not a good analogy, since the intelligent person would be able to write a program that is at least as good as yours, even if they aren't able to debug yours. It doesn't matter if the intelligent person can't debug your program if they can write a buggy program that works better than your buggy program.

We're not talking about the intelligent person being able to debug "your" program; we're talking about the intelligent person not being able to debug his own program. And if he's smarter than you, then obviously you can't either. Also, we're talking about a case where there is good reason to doubt whether the intelligent person's program "works better"--it is in conflict with some obvious intuitive principle like "mass murder is wrong".