Actually yes, at altitudes of 12,000 ft Oxygen will be necessary
At the time Adrienne did her legendary flight in 1921, Oxygen was probably not available in Aviation yet, so she probably just referred to her environment perception and did not add this to her checklist
The route she followed, that I have reproduced in the flight plan here, is mostly composed of paths following rivers in valleys at less than 11,000 ft.
Only a very small portion of the flight requires to fly over 14,000 ft for a short time, and then you fall again in valleys at less than 10,000 ft.
So also feasible without Oxygen, according to nowadays rules
Probably this may have been a key point for her success, going mostly West direction, and managing to stay most of the time in the valleys maze, beneath the surrounding peaks and high ridges, at less than 11,000 ft for most of her flight
Clearly audacious and intelligent, as she had no map to follow at that time