You are correct - two things happening here: 1. Picking up RF energy from far away. This is the easy part - cell phone antennas are already a big compromise and can be improved on if you increase size or cost. Instead of omni-directional antennas and low-power amplifiers, a directional antenna and low noise amp will work wonders. Cell phones already have extra power to get through buildings and trees; in this case that power would be used to go extra distance (because there won't be these obstacles).

2. Many users seen at once. Each beam is only a 15-mile-diameter circle. In the really remote areas where this coverage would be needed, I don't suspect that there would be too many cell phones - maybe a few hundred at most.

http://www.satmagazine.com/story.php?number=1026762698