Yes and no. The results I mention (see reference above) discuss learnability in the context of Computational Theory, so the branch of maths that looks at what is computable with languages and automata (a.k.a. the theoretical part of Computer Science).
Yes, it's entirely possible that we have missed something really important and when we figure that thing out we'll end up with a completely different Theory of Computation than we have now, and that may allow us to progress in learning concept classes that, today, are not learnable. That however, would be a revolution on par with Einstein's in physics.
Another thing that might save our collective ass, in terms of learnability, is that many of those results are assuming that P != NP. If that turns to be wrong, then those results will be off.
However, all this is very unlikely and in any case a) we can hardly expect such a profound re-interpretation of all that we know to happen within the next couple of generations and b) even if it does it remains the case that at this point in time everything we know suggests that there are some concept classes that we can simply not learn efficiently, at least not with computers.
Edit: what I'm really trying to say is that we may not understand human minds, but we're talking about computers here, so basically I agree with what you say, but with an added flourish :)