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?
If I remember correctly (it has been since 1998) the 16% value has something to do with entering confined spaces. I remember our "bang meters" checked not only for bad gasses (things that go BANG), but for O2. Seems as though the 16% value was considered the do not enter threshold without supplemental air.
Said meters actually checked for all sorts of things, and were able to determine the fuel/air mix for combustibility.
But like I said..... This is operating on 11 year old memories.