That's an argument for a research paradigm, its not an argument for the truth.
If there are fatal problems with Theory-A, Theory-A isn't true. No matter how much Theory-A might help with some other problem you have.
The CCTM is the research paradigm for modern AI, parts of cognitive science, etc. -- and insofar as it provides a clear set of assumptions to arrive at useful models, so be it.
Alexa can turn the lights on, for sure. She may even be able to reason a little (if-then-else, etc.). I doubt she will ever know what a "light" is, or what she is doing when she turns it "on".
That would require Alexa to have lived a human life, and to have lived in a deep and complex social/physical environment. There is no "logic" which can specify such things in a limited set of propositions: the effect of the world on animals is not merely to add propositions to their "set of beliefs".
Rather, animals are first traumatised by the world: their emotions, physical memory, instincts, etc. are all unmindfully coerced by their environments. Only with a peculiar sort of frontal lobe are those things expressible as propositions -- but they arent propositions, as evidenced by the infinite number of them required to capture the effects.
What we need before understanding inference, is to understand on what inference operates: the mental life created by the effect of the world on the whole mind of the animal.