She cannot just assume someone to be a God because they made an achievement that looks and feels impossible for her to do.
If that is how Godhood is decided on, then every strong person in the world will have the honorary permission to become a God.
By then, the term Godhood will hold no plausible value like it does now.
He knows what she is thinking and understands her well. Sango does not blame her when even he is not fully sure if what he says is true or not.
But there is no other way to describe himself in this world. He has the status of a God, a statue in his name and followers who worships him.
Sango's way of thinking is that the normal thing for him to do is introduce himself as a God to any native of this world because that is his heritage.
If they believe him or not is not his business to worry about, nor does he have the luxury of caring about it.