I agree with BookBurner, Chris and Ryel and from personal experience. It has more to do with the strength of your ankles than the material of the boot. Your ankles will become stronger if you train in running shoes versus boots because the extra “support” of the boots will hinder the muscle development. Just like relying on an ankle brace. If the brace does the work of the muscles, they do not need to develop further because they aren’t being trained.
It does help to have pack weights under 20 pounds, but with properly trained ankles, quality running shoes (I use Montrail Hardrocks) and good foot beds (I use SmartFeet) you can wear trail running shoes and carry loads above 20 pounds.
David Neumann