Yesterday I was shopping for breathable waterproof boots* and this is what the salesperson explained to me. The shoe material does NOT matter. The damp air from the foot goes through the membrane (Gore-Tex) to an intermediate "pocket" between the membrane and the outside shell of the shoe. Once the shoe is removed, the dampness begins flowing back through the membrane and into the air, thus drying the shoe.

Is this correct? Do shoes not breathe through the outer layer at all?

_{* - I call 'boots' any shoes, that are high enough to support the ankle, but mainly leather ones}