The braces form a lap joint at the X, like this:
The brace that goes over top acts as a solid beam because it is "capped", or bridged, below by the soundboard. The brace on the bottom needs the cap on top in order to have the strength/stiffness of a solid beam, otherwise it would be dramatically weakened by the notch.
I don't believe a cloth patch really accomplishes this, so I've never really understood the reasoning behind the use of a cloth patch.