I'm seeing them in other modes such as "Quick Match". Can you earn belts this way, as well?
Belts are improperly displayed when playing quick matches. You do not gain/lose rank for playing and your rank doesn't change, the belts are just misplaced on the loading screen. (If you're playing a quick match ffa someone on the loading screen should have your ffa belt rank, and same goes for 2v2, it's nothing more than a display error)