crab -
surface pressure is due to the weight of air above it squashing it down against the surface of the earth
Isn't that what our helicopter is doing? it sounds like the same thing to me only on a micro scale as opposed to a macro scale. There is more weight (atmosphere + helicopter) over that small area under the disc than there is over the area next to you (atmosphere) in the hover....
I'd also like to put this question out there. F=M.A if the air is changing direction under the disc (diverging), by definition it's accelerating (change of direction/velocity). So a force is being applied to that air. If this is not due to a pressure gradient, what causes it's change in direction?