Where on Earth did this "set the trem flat on the body" stuff originate?
It's sheer nonsense. That it can be done with a Strat tremolo is a mere accidental by-product of the design. In other words, it's a bug, not a feature - and is to avoided unless the player doesn't want to use tremolo at all (in which case he won't need to attach the arm anyway).
No other design of vibrato allows such a setting. Why would it ever be a desirable feature - except to render the trem unusable?