A 17-year-old pilot and two friends died in a crash in the Alabama woods Tuesday night, less than a mile from the Walker County Airport in Jasper, northwest of Birmingham. Sherrie Smith, the mother of the pilot, Jordan Smith, said he had his own key to the Piper PA-30, denying the authorities’ assertion that the plane had been taken without permission. Ms. Smith said that the plane’s owner had let her son fly it many other times and that her son was one test short of earning his private pilot’s license. She said that the plane was parked behind a security gate, but that her son had been given a security code to access it. Brandon Tyler Ary, 19, and Jordan Seth Montgomery, 17, were also killed in the crash. The plane left from the small airport around 10:30 p.m. in overcast skies and a low cloud ceiling, the airport manager said.