That is true. When the ignition points are closed in the Kettering system, current from the battery flows through the coil, thus building up a strong magnetic field in the core. This does not happen instantly, for a coil tends to discourage any change in the current that flows into it and will thus produce a voltage to oppose that change. So during the 'dwell' period when the points are closed the coil is allowed to take enough time to build up a substantial magnetic field.
When the points _open_, however, the current is cut off instantly, or nearly so. Again the coil discourages this change in current and tries to maintain it by producing a very high voltage across the ignition points to try to push current from one to the other. In this it partially succeeds, and that's the spark we see between the points when they open. But we really want our spark to show up across our spark plug's electrode, so we place a capacitor between the points to store most of that extra current. We get the current back, however, when the capacitor (okay, condenser) discharges its energy into the coil. That coil is surrounded by a much bigger coil, and the current from the condenser produces a pulse of magnetism in that larger coil to provide our spark plug voltage.
The flywheel magneto is another sort of animal, though the dwell is just as important. That's because our coil is used as a generator coil: it produces current when the flywheel magnet passes by and the points are closed This current circulates through two coils: one is the generator coil, and the other is the 'primary' coil of the spark transformer (also confusingly called the 'coil.') This current makes a strong magnetic field that also soaks through the 'secondary' coil, which has a zillion turns of very fine wire wound on the same iron bar as the primary coil.
When the ignition points open, this strong magnetic field that has soaked through the secondary coil suddenly disappears. Since the rate of change of magnetic field determines the voltage generated at the terminals of the secondary coil, and that voltage is around twelve thousand volts, we'll get a spark across our spark plug's electrodes as well as a dandy shock if we're touching anything we shouldn't.
The trouble is that lots of variations of these systems are possible. Sometimes the primary, secondary, and the generation coil are wound onto one big lump, as in a lawnmower or my old Peugeot moped. Sometimes the generator coil and the primary and secondary coil are separate, as on the noble Trac Clipper.
Right now it's too dark to work on the bike, but I'll open the point gap to some experimental measurement, see how things go, and report.
Everyone has been very helpful, and thank you. Please continue to add advice if you think of anything. What are the symptoms of an engine whose timing is insufficiently advanced?