Yeah, I think someone is getting numers mixed up.

Normal air is 21% oxygen - at any altitude. The problem is the partial pressure drops with altitude, so there's less barometric pressure... blah blah blah. I'd be BS'ing if I said anything else, but I know that's the big problem with elevation and altitude sickness. I'd hazard a GUESS that the partial pressure of O2 in the blood needs a pressure gradient, and the drop from altitude makes it harder to transfer.

16% is the amount of oxygen in the breath exhaled.

FWIW, I have absolutely NO idea how "little" oxygen is needed to keep alive. I know that you can get up to 100% inhaled oxygen, but not the other way. Anyone?