As a complete layperson, I suspect osmosis may be a good counterexample. Channels react selectively to various compounds, but water can probably pass through the membrane more easily.
Wikipedia (heh) seems to support this idea, but my gosh is this all complex.
> Compared to ions, water molecules actually have a relatively large permeability through the bilayer, as evidenced by osmotic swelling. [...] Small uncharged apolar molecules diffuse through lipid bilayers many orders of magnitude faster than ions or water. This applies both to fats and organic solvents like chloroform and ether. Regardless of their polar character larger molecules diffuse more slowly across lipid bilayers than small molecules.
But then any model has its limitations, doesn't it. I think hydrogen can go through metal (and probably walls), so you could say walls are not a good model for walls.
Wikipedia (heh) seems to support this idea, but my gosh is this all complex.
> Compared to ions, water molecules actually have a relatively large permeability through the bilayer, as evidenced by osmotic swelling. [...] Small uncharged apolar molecules diffuse through lipid bilayers many orders of magnitude faster than ions or water. This applies both to fats and organic solvents like chloroform and ether. Regardless of their polar character larger molecules diffuse more slowly across lipid bilayers than small molecules.
https://en.wikipedia.org/wiki/Lipid_bilayer