Dostoevsky was a great writer and thinker, and FB fact checking is hardly the arbiter of truth. If you want to understand what the man really said and learn how his writing can span time and culture you could do worse than watch Rewire the West's current series on Dostoevsky and his wider influence and instructions.
https://www.youtube.com/playlist?list=PLQNV7Ov7-4efX1byYNoO54Q8U0ZXCcjy2
He might well not have said it, but I wouldn't choose Facebook as the arbiter of truth.