often seen in the street without a hat

It doesn't seem a good idea to wear constricting clothing that constricts in the same place 24 hours a day simply for the sake of the skin. But trying to think about where the bits of the lymphatic system actually are, I don't think that a tight band would restrict it, because the band basically goes round the ribs, and the ribs are on the 'outside' of the body, as it were, with vessels inside them.

Ah, Google points me to some bad science - it looks like this one is an urban myth.