A purist family just is terribly unlucky, and their only (surviving?) heir turns out to be a squib. To hide this, he is raised abroad and when he comes back, he pretends he is a wizard—carries a wand, knows all about herbology and potions and arithmancy or whatever, and even has an ~exotic magical pet! Sure, he can't apparate (bad luck once when drunk I'm missing a toe!) and he finds quidditch and dueling overdone, but he's totally a wizard.

Totally.