Ford doesn't specifically tell us why 20" wheels have a higher tow rating but we do know that part of industry testing procedure is stability. So the best guess that I have is that the larger wheels are stiffer and therefore more stable.
The interesting thing is that the F250 comes with 18" wheels and the exact same size tires as they put on the F150 but has a much higher tow rating. The F250 tires are LRE whereas the F150 comes with either P series or LRC tires.
Maybe the extra 4 ply rating is enough to justify the difference. But we will probably never know for sure.