The boy, who has admitted causing £30,000 worth of arson damage and burglaries, was sent by the county council to the Small School, Humberside, in May. The school charges local authorities £44,000 a year for rehabilitating children with behavioural difficulties, the paper says.
Its curriculum includes sports and adventure courses, some of them in Spain and Scandinavia.
Ken Foote, deputy director of social services at North Yorkshire CC, said the school's programmes were approved by the Department of Education. Other methods of curbing the boy's anti-social behaviour had been tried unsuccessfully, Mr Foote said, and since joining the school he had not re-offended.
But Tory MP for Ryedale John Greenway told the paper the right approach should be custody through the secure training orders for 12 and 13-year-olds, which the government is to introduce soon.