It is not true that no work is being done. The rotor blades do a LOT of work pushing air down and thus causing the helicopter to accelerate upwards at 9.80665 m/sec/sec in a gravitational field that is causing it to accelerate downwards at the same rate. So ... helicopter stays motionless, air moves. From the frame of reference of the air, the helicopter is moving quite a bit and is doing a lot of work.
I think the aerodynamics of it all may be a bit more complicated than that simple explanation, but you get the idea ...
The exact same question was asked recently in the form of "if I push a box across the floor against friction, I am doing work, but in MY frame of reference the box isn't moving so I'm actually NOT doing any work. What gives?" In his frame of reference he is doing work moving the floor under him. In both his question and yours, you can't get rid of the work being done just by changing frames of reference.