Hmmmm ... the idea that short-scale basses were designed for use by students (and other younger players, and kids, and players with smaller hands) would have come as something of a surprise to the many firms who produced them, and the very many grown-ups who played them.
That is a shockingly Fender-centric view of things.
Just as an example, all Hofner basses from the 50s, 60s, and 70s were short-scale (30.5"). That's all of them, not just the hollow-body basses, not just the violin bass.
Presumably Fender's view was that Paul McCartney was a student (or other younger player, or kid, or player with smaller hands) since he didn't play a Fender.