I think this is the correct explanation.
There is a potential difference (voltage) between the helicopter and the powerline. The powerline is negative, meaning it has more electrons than the helicopter, which is positive. Negative flows to positive meaning the electrons flow to the chopper through the wand to bring it up to the same potential as the line. Also, ground is relative. In one sense the helicopter is at ground potential in relation to the line since it has fewer electrons than the line. However, it has more than the earth below it. Helicopters in the air can pick up a huge static charge - I know from experience having hooked a cargo net on a hovering chopper a few times.