This would involve proving that humans exceed the Turing computable, which would mean proving Church-Turing thesis is false.
Because if humans do not exceed the Turing computable, then every single human brain is existence-proof that AGI is intrinsically computationally tractable by demonstrating that sufficient calculations can be done in a small enough computational device, and that the creation of such a device is possible.
Their paper accepts as true that Turing-completeness is sufficient to "computationally capture human cognition".
If we postulate that this is true (and we have no evidence to suggest it is not), then if their "proof" shows that *their chosen mechanism can be proven to not allow for the creation of AGI, then all they have demonstrated is that their assumptions are wrong.
Well, pregnant women create such systems routinely.
Due to the presence of the weasel word "factual" (it's not in the sentence I quoted, but is in the lead-up), no contradiction actually arises. It may well be intractable to create a perfectly factual human(-like or -level) AI -- but then, most of us would find much utility in a human(-like or -level) AI that is only factual most of the time -- IOW, a human(-like or -level) AI.
Trying to get the most out of tools that sit somewhere between "the killer robots will eradicate humanity", " there goes my entire career", "fuck that guy with the skill I don't want to develop, let's take his career", and "I'm going to be so fucking rich if we can keep the wheels on this" is exhausting.
And the cognitive science thing.