My lens experiments have enough variance in focal length to prove the theory right.. Lenses with shorter focal length act the same, as long as the entire surface plays along, like said earlier. Lens distance to the source does not matter (at least, within the focal length's I used during my experiments..). Apparent surface brightness is not affected by source-lens-distance..
Extremely short focal length's bring difficulties for the shape of the lens: Apart from the fact that they need to be extremely aspheric, the extreme radius of curvature brings a limit as well.. The shorter the focal length, the harder it is to make the entire surface play along.. (needed for throw..)