I am familiar with that portion of the Gila Wilderness, and there are a few odd things about the story. But first, the gentleman did know enough to keep himself alive, and he did do enough of the right things.

"failure of the filter system" is not an emergency, since boiling is just as good. I am surprised that he evidently became dehydrated. The Gila Wilderness, especially the Middle Fork, is extremely well watered. The numerous fords on the Middle Fork trail are typically one the biggest obstacles to travel. The water is quite good, especially in the upper reaches of the Wilderness where he was. I usually drank untreated water there.

Backtracking is not his best option,but any map will indicate that Willow Creek is on the West Fork of the Gila. A straight down canyon walk, again plentifully supplied with water, would have taken him back to his car.

From the story, it seems clear that he could improve his map reading skills.

One other thing. People often underestimate how difficult it is for airborne observers to spot someone on the ground. A signal mirror, or the mirror on the compass in your 10 essentials, is far, far, and away the best way to get the attention of someone in the air.

One final comment. He couldn't get into the cabin? In my misspent youth, I was the ultimate ultralight backpacker, carrying a Forest Service master key on my compass lanyard. It opened the door to the resolution of many problems.