I do not know if I would claim the small signal BW is guaranteed by design, but the it is designed to be much greater than the video BW (about three times as much).
Video BW is for AM and rise/fall time: they are interrelated. The rule-of-thumb is that rise time is related to bandwidth by the equation:
Rise time = 0.34/Bandwidth
This of course varies a bit from system to system, but it is a good approximation and starting point.