The quantity of storage in your canteens is not a factor in the area in which he was hiking. He was basically hiking along the Middle fork and (potentially) the West Fork which are permanent, crystal clear trout streams. Even the trail from the Middle Fork to White River RS is well watered. You can stop every five minutes to get a drink or brew up tea, which is what makes this area of the Gila Wilderness so attractive.

Considering he flew from Houston (sea level), altitude may well have been a factor, as Pete pointed out.