My gut feel is that if you hit hard enough, the pressures that I use will pinch flat. I'm one who had side wall cut on my car three times. Two of them were not even soft walls, they were Good Year GT3. Other one was a soft wall Continental Premium Contact 2. They were all with recommended pressures - 30 psi.
On bike, I had got only once, that was on my MTB, on a bad bunny hop over a cemented road with speed hump with pressure less than 25 psi on a 2.25" 27.5 tires/tubes. Otherwise, I had run 23c with extremely low pressure on nasty and unfamiliar roads in the night (read Bliss In The Hills Periya downhill section and beyond). Then I had occasionally flown over very bad potholes, rumble/rubble speed breakers as I couldn't brake on time. At times, it even shook me off the pedal/saddle. Gana and Putta were witness to many of these experience along with me. Puncture was the last thing on my mind. They know how low I ride in pressure.
Having said that Putta was telling me just yesterday that he still suffers from pinch flats if he rides on low pressure. This made me think that I'm probably doing something that others are not doing. I, for instance, glides over loose sands (on straight), floats over piles of sharp broken pebbles. So, this instinctive easing of the weight on the wheel that faces an obstacle could be the thing. it is hard to explain. It is like skating on a smooth surface and suddenly you hit a patch of rough patch. Tendency is to fall, but you eventually learn to not fall. It is instantaneous. I believe that this must be the key. If someone can find a research material on it, it will be great (I miss Sree these days :().