The driver circuit is controlling the ground/ trigger side of the coil. This circuit is closed when no power is applied from the processor, If the coil were to receive power it will be grounded through the driver inducing a high current flow. This being why the coil should not get power when the MS is not on.
Even with external triggers as with multi coils this is important. Most of my work with MS has used either Bosch or Mitsubishi drivers, and I have had my seared fingertips even with them.