electronics 101 at play here.
the points are the source of 'ground' for the coil. when they close, there is a complete circuit.
if you have that dizzy off in your hand and put power to the coil, and the points are closed.. the body of the dizzy will be at the same potential as the top of the coil
certaintly no mystery here.
have you checked key switch and resistor contacts.
reading voltage on a meter is 1 thing. haveing a good enough connection to conduict some current is another.