Why dump the shells at all.
Why not get the F out of Dodge and then dump them.
I never quite understood that.
It doesn't have any bearing on who the shooter was, it just seems weird (to me, at least).
I imagine that the gunman would quickly come to the conclusion he needed to reload ASAP before anyone decided to jump him.
Or in case anyone else was nearby with a firearm of their own. Texas has something of a rep for being Texas, after all.
And why keep fired cartridges in your pocket? They don't help you escape, and are evidence that you fired the pistol that your carrying since (at least) you put your pants/jacket/shirt on.