Well, for one thing, fruits are not composed of
distilled water.
Soil water, or rain or dew absorbed though leaves,
all usually contain detectable minerals, many of
which are necessary for plant function and are
translocated to fruit in water.

Also, minerals are frequently 'inorganic,'even
when essential to life, like calcium, magnesium,
zinc, selenium, copper, iron.. This is because
'organic' refers to compounds containing carbon,
and not all minerals do.

Putting distilled water on one side of a permeable membrane adn
a colored salt solution on the other side will
equilibrate with the salts crossing over until there is
an equal osmotic pressure on both sides of the membrane.
(Dropping tissue samples in distilled water is a lab NO-NO unless you
want to explode the cells.)

Our GI tracts are not passive permeable membranes, in fact,
they have a lot of selection mechanisms, but cells can only
deal with so much, so I steer away from distilled water
unless the alternative is Giardia infested or other
similar problem.

Distilled water tastes flat because it lacks
dissolved oxygen. I haven't seen any direct evidence
of needed oxygenation in gastrointestinal fluids,
but it's a project for somebody!