I used to fly a 48" delta winged glider that had a catapult launch. The catapult would launch it at about 120mph. I could fly to about 300 feet in a nice vertical arc, but as soon as I yanked back on the elevons, the rather light plane would turn sharply and slow down significantly, due to the very effect discussed. A non delta wing would have been unable to maintain airflow over the wing because the high AoA (20-25 degrees) would have been far more than the 12-15 degrees that straight or swept wing can take.
In other words, the Delta wing kind of acts as a giant vortex generator: https://en.wikipedia.org/wiki/Vortex_generator
That's not quite right either. A wing doesn't stop flying when it stalls, i.e. when the angle of attack exceeds the critical angle of attack. What does happen is that the coefficient of lift starts to decrease instead of increase what increasing angle of attack, and with sufficient angle of attack the coefficient of lift can become too low indeed.
A wing in stall can be flown, but it's tricky. Controls are inverted, natural stability of the plane doesn't really work anymore. It's not a situation you normally want to be in, but the plane does not suddenly fall from the sky.
The article referenced also talks about control inversion, interestingly. So yes, a stalled wing can be "flown" but not in the same way that the original question was referencing.
That's not the case for a delta wing in the regime that the article talks about. Increasing the angle of attack still increases the coefficient of lift.