[Jim in Wisconsin]

At least for a part of the time that the coil has current flowing through it, both points are closed. During that time both would have to "bounce" open in order to break the circuit. During the time both sets are closed, I guess you could say the chance of point bounce is cut in half, not doubled.
First, one point closes which allows current to flow. Then the other one closes which does nothing. Then the first point opens, which does nothing because the second set is closed. Then the second set opens which stops the current and as the magnetic field collapses in the coil, a large voltage spike is created for a short time.