A dog exposing their belly to a human, especially their human(s), is more about being comfortable and relaxed than submissive. It can also be playful/silly behaviour towards their family.

I have a dog that likes to go paws in the air just to silly. The tail will be banging anything in range and dusting the floor. The moment I get down for a belly rub, tail stops. If talk silly back and offer a treat I get an explosion of happyness and cooperative mood.