I'm having trouble understanding what is even being claimed. Electrons are moving, without the movement of the electrons there is no electricity travel, without the wires there is no flow of electrons, so what does it mean to say that electricity doesn't travel through wires?
Is the claim just that the electricity, by way of fields, travels at a rate much faster than the electrons themselves are traveling? That seems like a reasonable claim. But "electricity doesn't travel through wires" seems rather suspect.