websites wrong.. you never put your foot down while moving. Easiest way to break your freaking ankle.
I know dirt bikers in motocross do but if you notice they are wearing armour plated boots even so they arent exactly riding the ground..

I'd rather dump than put my foot down and break my ankle. (been there done that.. learned my lesson not to put my foot down in a turn to support traction)

No, the website, test, and instructors are ALL correct.  If you're on an unstable surface you use your feet to gain stability.  You don't ride at 75mph with your feet down.  You don't hammer through turns with your feet down.  You don't try and evade objects with your feet down.  If you're on something akin to ice or gravel you creep along at idle, if that fast, and use your feet to hold the bike up because at that speed it sure isn't going to do it all on it's own.