There is a difference between people saying "Draven falls off late game" and "Draven's damage falls off late game". Usually people use them to mean the same thing because the standard "falls off late game" guy, Lee sin, falls off because his damage scales poorly (thus falling off is most commonly in reference to damage). Falling off just means he becomes less effective after a certain point in the game, but could be for any number of reasons; i.e. lack of damage, lack of range, lack of ability scaling, lack of safety, lack of items, etc.
Draven does fall off late game, because he is a fairly immobile, short ranged ADC, whose main damage requires him to walk into very obvious targeting icons that are basically a big fat "hook me right here!" signs. His damage is extremely high, but so are champs like Kog, Vayne, or Jinx, each of which are much safer end game because they have either stupidly long range or really high mobility on top of their high damage. If you're good with Draven, yeah, you won't fall off as hard late game because you can use him better, but in comparison to most other high damage threat champs he falls off.