This is not true. It is not the mere lack of oxygen that is the problem, but that the oxygen is at too low an absolute pressure to be absorbed efficiently by the lungs. A small gain can be made with a pressure demand regulator, which allows the lungs to operate a few mmHg above ambient pressure, but not much, or you don’t have the strength to exhale against that pressure. Wrapping the entire body in a pressurized suit allows the lungs to operate at sea-level (or whatever…6000’ is used for airline cabins) pressure. At this altitude, the climbers would need only atmospheric oxygen concentration, so the suit could be supplied by a compressor. (as airliners do) No oxygen bottles or concentrator would be needed, just a power source for the compressor.