That's different than what I learned. I read that the purpose of a flyback diode (in addition to preventing arcing across switch and relay contacts) is to prevent negative potential getting back to the power supply. I agree that the coil becomes a generator, but it generates an opposing voltage to that which was applied to it previously, which forward biases the diode, basically shorting out this new generator in the circuit and discharging it's stored energy very rapidly.The diode keeps the current flowing (into the power supply) so that the inductance can discharge slowly.
Without the diode then the inductance creates a rapidly reducing discharge current. The rapid change of current causes the inductance to try to generate a voltage high enough to keep the discharging current flowing slowly. The high voltage is created when the rapid change in the magnetic force cuts across the windings of the coil making a generator.