I've seen people do YYYY/DD/MM, so your friend's format isn't foolproof. OTOH although I'm sure some insane person somewhere has done YYYY-DD-MM I've never seen it so YYYY-MM-DD should be safe.
Some languages pronounce the date as year, day, month so some people write YYYY/DD/MM. Since both YYYY/DD/MM and YYYY/MM/DD make sense to different people, neither should be used.