This is the main point of a nice article by Roald Hoffmann, that I posted about in the early days of this blog.
I experienced this a few weeks ago. I have been working on a paper with my postdoc Nandan Pakhira about the viscosity of strongly correlated fermion fluids, focussing on the Hubbard model. A basic issue I got quite confused about is the relation between the momentum, Bloch wave vector, and velocity of an electron in a Bloch state. Yet, I when I taught this to my solid state physics class I was reminded of the correct result.