I would not even expect there to be a problem; it only seems that way if you naively imagine that trees contain continuous, open pipes from top top bottom.

A bucket brigade works just as well up ten flights of stairs as up one hundred. So does a system of opening and closing valves.

We can pump water from a bucket on one floor of building to a bucket on the next floor easily. Then we can repeat the same thing at the next floor; the pressure from the numerous floors above doesn't factor in because there isn't a connected water column.