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I don't think his explanation for why a chair pushes back on your hand is quite right, either. I've mostly been told that material solidness comes from the Pauli exclusion principle, not electrostatic repulsion.
I don't know quantum mechanics, so I don't have a good perspective on the problem, but the electrostatic explanation has always seemed lacking to me. The electric charge in a neutral atom is fairly well-approximated by a symmetric sphere of negative charge with a bunch of positive charge at the center, so two atoms shouldn't experience much electrostatic repulsion until their electron clouds overlap. At which point [I've heard] the PEP should dominate the electrostatic force.
Can any physicists or physics students comment?
I note Fyenman above is quoted as saying, "There's other forces involved, connected to electrical forces" in the context. One can quibble about how "connected" the Pauli exclusion principle is to electrical forces, but he is explicitly acknowledging there's more going on than just the immediate results of the electromagnetic force, in the midst of an extemporaneous explanation as to what's going on with magnets.