I don't think that's what he was referring to. Apart from not being "fast", it's not a program in the sense being discussed here, given the article is about com

I don't think that's what he was referring to. Apart from not being "fast", it's not a program in the sense being discussed here, given the article is about computability. It's an oracle turing machine rather than a plain turing machine, and oracle turing machines can trivially side step computability questions by having the oracle evaluate the noncomputable function. (This is of course not relevant to the oracle you suggest as that doesn't evaluate a noncomputable function, but it's relevant to what sort of "program" Aaronson is talking about here.)