Danger of Saturation of Primary Coil in a Flyback
Yes, you understood correctly. At saturation it is like the inductor "loses" its inductance. What you're left with is only the Rs (ESR) of the inductor. For a quality inductor Rs will be very low resulting in a large current and possible damage to inductor and/or FET.

An inductor stores electrical energy as magnetic energy, when the inductor saturates it cannot store more energy since it is "full". The core material of the inductor (if there is any) has reached its maximum magnetic flux and cannot accept more.