Dehydrated, starving and with one-third of his body weight lost, Mr Bogucki, 33, was lifted out of the Great Sandy Desert by a helicopter team after he had been reduced to scratching for water around billabongs and surviving on plants and tea made from eucalyptus leaves.
The 33-year-old fireman from Alaska had been given up for dead by Australian police, Aboriginal trackers and a search team from the US who had flown in with three bloodhounds and retrievers.
"I felt really alone, not desperate but just without hope at some point," an exhausted Mr Bogucki said from his hospital bed in Broome, on the north- west Australian coast, where he was flown for treatment. The month-long search for Mr Bogucki in the outback has captivated Australians, and his discovery was hailed as one of the remarkable feats of survival.
But questions were being asked, especially by Western Australian police who believed at one point that Mr Bogucki was deliberately evading searchers to test his survival skills. And there were also suggestions his adventure could be linked to a publishing deal in America.
Police want to know why the American walked alone into one of the world's most inhospitable regions, whose remote rocky ranges, red earth and searing temperatures have claimed many lives. Superintendent Steve Roast, of Broome police, said: "We have to face facts. Mr Bogucki went out there alone. It was an extremely irresponsible thing for him to do."
Mr Bogucki had apparently set out to walk 250 miles across the Great Sandy Desert, where few humans venture, to Fitzroy Crossing, a town on the main highway through the Kimberley region. He said yesterday: "I wanted to spend a while on my own with nobody else around, to make peace with God."
He was last seen a month ago. On 26 July his bicycle and backpack were found at the Sandfire Roadhouse between the Indian Ocean and the desert on the highway 150 miles south of Broome. Police with Aboriginal trackers mounted a land and air search, but called it off after a fortnight. Mr Bogucki's parents in America hired a team called the 1st Special Response Group - eight men and women and three dogs - to fly to Australia and resume the search. The team was led by Garrison St Clair, known as "Gunslinger".
Their arrival on the scene caused tension with the local police, who feared the overseas searchers, too, could disappear in the unfamiliar terrain. Car hire companies in Broome, whose four-wheel-drive vehicles had been damaged in the earlier search, declined to do business with the Americans. A Broome hotel company finally rented them its four-wheel- drive tourist coach.
Helped eventually by police, the Americans set up a base camp near the Edgar Ranges, a series of deep desert gorges south-east of Broome along Mr Bogucki's probable path.
After three days their search proved fruitless and they were about to pull out last weekend. Then a media helicopter alerted them to a pile of human belongings in a blue tarpaulin and abandoned in the spinifex grass near the ranges.
They were Mr Bogucki's empty plastic water bottle, sunscreen, tent, boxer shorts, a T-shirt, a Bible and a notebook containing rambling written thoughts. "They're the thoughts of a bloke obviously in isolation," said Senior Constable Lindsay Grateorex, of Broome police. "It goes all over the place."
The fresh discovery convinced searchers Mr Bogucki was alive, but seriously needing help. Yesterday morning a helicopter chartered by Channel Nine, a commercial television network, was the first to spot him staggering through the gorges. "Gunslinger" St Clair said: "I think he wanted to be found. He said he thought he was in trouble several days ago, so he lightened his load."
Mr Bogucki said he survived by eating wildflowers and fruit. His cadaverous appearance suggested the claim might not be far-fetched. Asked if he had found what he was searching for, he replied: "Before I started out I really didn't know what I was looking for.
"It's still going through my mind the things I've seen and experienced. I feel satisfied that I stretched that edge, whatever it was that sent me out there in the first place. The only feeling I have right now is a feeling of confidence that God will take care of you."
Broome police are unlikely to appreciate such New Age reflections. They say Mr Bogucki did everything tourists are warned not to do when venturing into the outback: Tell people where you are going, carry enough water for your entire journey and stay near marked roads, especially if you become lost.
Last night the police had turned to another search, for a boat, lost off Broome's coast.