Regarding you spending a night above 26k ft, I guarantee that you were in nearly peak condition, trained for that hike, and spent time at high altitude getting acclimated (or you live at high altitude and were acclimated unconsciously). Even then, most trained hikers at 26k ft can only sustain a walking pace for a length of time. These geese retain enough aerobic power to maintain flight at that altitude. Saying that you were a "bit knackered" the next day is not recognizing how close to the edge your body was- did you measure your oxygen saturation levels and would you care to share them so that everyone can see that you calling yourself a "bit knackered" had you well into the clinical range for hypoxemia, and every doctor in the world would tell you come back down the mountain?
While not everyone will die, the zone above 26k ft is literally called the death zone. The lack of oxygen is like a poison, every body handles a different amount, but 26k ft is certainly high enough to say it "kills humans." People have survived cobra bites as well, but most people agree that cobra venom is lethal.
>At 26000ft, the standard barometric pressure is 38 kPa (287 mmHg). This means that there is 38% of the oxygen available at sea level. (from https://baillielab.net/critical_care/air_pressure/)
I camped a night above 26000ft without supplemental oxygen (it packed up) and was ok but definitely a bit knackered the next day.