When people say she's short range that doesn't refer solely to her auto-attacks.
Corki has a way to poke outside his auto-attacks, Draven has abilities outside his auto-attacks, Ezreal has abilities outside his AA range, Kalista has damage outside the range of her AAs, Miss Fortune has damage outside the range of her AAs, Sivir has damage outside the range of her AAs. Kog'maw, Tristana and Jinx have ways to damage beyond their normal AA range (Koggy W, Trist passive, Jinx Q), Quinn's thing has less to do with range, and more with her design. Lucian has less solely thanks to heavy-handed nerfs that lacked forethought on Riot's part, and Urgot has ways of damaging outside of his AA range. And hell, while we're here: Ashe has ways of damaging outside her AA range, Caitlyn has ways of damaging outside her AA range, and Varus has ways of damaging outside his AA range.
Vayne has literally no way to contribute any damage outside of her AA range while other ADCs do, making her 100% limited to a 550 range, a range that is considered by many people to be fairly short when you have nothing else to do with it. Medium range at best.