Indeed it is not a correct assumption. OXY Masks need to be demonstrated only on flights cruizing higher than FL240, the reason being that if pressurization fails below that level, the flight crew (who will put on their masks) will bring the aircraft down below FL120/12000ft within the time that you remain conscious, which for FL240 is around 5 minutes. So, even if you do not put on the mask, you may feel dizzy for a while, but as the aircraft descends, your body will receive more oxygen and any symptoms pass again.
If it were indeed an unpressurized flight, it would have stayed below 10000ft. This occasionally happens if there is something wrong with the pressurization system.