why does box bracing make the box quite?

Yes.

Figuring how out something will affect an SPL score is a pretty complex task...anything that lowers a panel's resonance or obstructs airflow could change it...who knows until you get on the meter. It could be that the box's resonance is reinforcing the rear wave in just such a way to contribute to a higher score.

Same thing happens with adding sound deadener - sometimes you see a gain, sometimes you don't.