As mentioned earlier it is the partial pressure of oxygen that matters.
At the surface we breathe air at roughly 1 bar ambient pressure, so 21% oxygen multiplied by 1 bar gives a partial pressure of 0.21 bar.
At a pressure altitude of 38,662 feet the ambient pressure is 0.2 bar, so 21% oxygen multiplied by 0.2 gives a partial pressure of just 0.04 bar.
Most of us would be incapable of thought or meaningful action, and most likely we would be unconscious with a partial pressure of <0.1, so no wonder the TUC is measured is seconds with a partial pressure of 0.04.
Breathing 100% oxygen at ambient pressure at 38,662ft gives a partial pressure of 0.2 bar, almost the same as at sea level - you really don't need pressurised breathing systems at this height.
By 44,647ft the same 100% oxygen at ambient pressure delivers a partial pressure of 0.15 bar, about the same as flying an unpressurised aircraft at 10,000ft without oxygen - probably not ideal for dealing with anything that needs a high degree of concentration, decision making, or fine motor skills.
There is a big difference in performance between the oxygen masks supplied to pilots versus the passengers. In medical use, rubber masks with a reservoir bag only deliver oxygen up to about the mid 80% mark. These masks are nearly identical to passenger masks in how they work. Pilot masks are a better fit and deliver oxygen via a high flow regulator and not a reservoir bag so should deliver much closer to 100%.
So, at 38,662 feet the passenger is only getting 0.17 bar partial pressure which may not be enough for anyone with pre existing health problems. The idea that even a small amount of oxygen will help stave of brain damage even if unconscious only holds true if you have an open airway to actually breathe through, and I suspect that strapping unconscious people upright in seats is a great way to ensure that their heads tip forward, closing the airway.