MK Dons held the cup after taking over the Wimbledon franchise, AFC Wimbledon complained saying that they were the true Wimbledon, in the ennd MK relented and handed the cup over to them.
A technicality, I know, but that's what makes it a ball acher.
But they didn't win it - AFC are not even the same club,
Using your logic the last non league side to win it are Portsmouth because they were non league once. and if they gice the replica to Havent & Waterlooville they are therefore the last non league club to have won it.