Some kids have died at camps like this. The link is the story of a 16 year old who died in Arizona in 1994.
He had to hike for miles a day and sleep with no blanket or sleeping bag in temperatures below freezing. He had no food for 11 days out of 20, partly as a punishment for being sick.
He complained about being sick for weeks - stomach pain, falling down, hallucinations. On the day he died, it took him an hour to crawl 20 feet to the fire. He died from an infection from a perforated ulcer. The staff were standing around making fun of him when he collapsed for the last time.
The owners of the camp pleaded guilty to negligent homicide. One of the counselors was convicted of felony neglect.
Earlier this year, a 12 year old suffocated to death at a wilderness camp in North Carolina. His death was found to be a homicide.