Okay, I have a theory as well, though I doubt it would work.
Maaaybe the chances of tripping changes depend on the
surface the character is standing on. I know that possible "air tripping" thing may outrule this theory, but that seems extremely rare - moreso than normal tripping.
Anyhoo, recall the Olimar - Special Moves update on the DOJO:
From Sakurai:
As long as there is ground beneath your feet, you can reach down and pull up a Pikmin, but be aware that certain Pikmin are more likely to appear in specific types of flooring.
So if such variables for Olimar's Pikmin Pluck could exist, maybe the same for tripping?
Now I don't know if you guys been testing this on the same stages or what.... But if I recall correctly, somebody said the Ice Climbers tripped more often on their glacier. So maybe if you guys take one character and try several different floorings, maybe the tripping odds will change slightly?