Tim, the switch DOES ground the points. It grounds them through the other set of points AND the coil primary attched to them. It is easier to merely say it connects the two sets of points together, but in reality when you connect them together you are grounding them.
Metty, is there any chance it is not running "properly", but running on one cylinder? If it has a bad set of points AND an open circuit in the coil primary, the switch wouldn't stop the other cylinder. That would be a very rare coincidence. However the continuity check to the armature plate that I previously suggested would find that.
Personally, I think you have a broken or corroded wire, just enough of a connection to fool your continuity tester, but not enough to carry the current involved