I think the author may have been referring to time dilation due to relative motion of the clocks as opposed to gravity. In that case, to an observer on the ground, the clock on the plane goes slower than a clock on the ground.
EDIT: Flying clocks around: https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experim... If compared to a clock remaining on earth, then it depends on the direction the plane is flying which effect wins.