I thought they might have some sort of "reverse osmosis" mechanism in
their makeup to take in seawater at 4% salt, remove some fresh water,
and then excrete a more concentrated salt solution.

There are trees that do something like that, notably tamarisks. They
grow near brackish or alkaline water sources, and take up the salty
water through their roots. They excrete the excess salt in the form of
salt crystals, which are found all over their branches. The water that
they transpire Is fresh. Due to the humid transpiration, people find
it very refreshing to sit under a tamarisk tree in the desert. That is
why Abraham planted one in Beersheba.
Iris