I almost never rinse off the glass, can't see any point, once you know what you are doing you just don't need too.
It may be more of a problem with flock bristled brushes, ie, they are more densely packed at the tips, possibly holding more contaminants.
The Salmon brush tends to rinse very clean because of the nature of the bristles.
The glass that beads must surely have some kind of water repellent finish on them, on some windows that predominantly bead up, on the windows that open out at the bottom so that when it rains they will always get wet, often sheet up (maybe not over the entire surface though) and the vertical panes either below, to the one side or above still bead up.
My conclusion is that the constant weathering serves to erode whatever this finish is, ergo the glass begins to sheet.
But where rinsing is concerned, I haven't found the need to rinse off the glass.
Ian