Knowledgeable skeptics have been voicing concerns about neurons not being the right level of abstraction to look at for decades. See, most prominently, Chomsky, and by extension Gallistel.
Gallistel wrote a book 'Memory and the Computational Brain,' in which he argues that neural storage and computation via synaptic strengthening alone is implausible, and that the brain must have a real read/write memory. He points out that genetic material is an ideal substrate for such a capacity...