Why do some PCBs put vias around mechanical through-holes?
If the screw (which should be smaller than the hole) is exactly in the middle of the hole, it won't touch the plating. So you can't rely on this.

Instead, they put a few openings in the solder mask (green paint) around the hole, which must be covered by solder paste so the thickness increases and it raises above the mask. It is not necessary to make it a via, but it make a shorter path between the bottom/internal ground layers and the screw.