On October 11, 2003, at 0835 mountain daylight time, an Aviat, Inc., Pitts S2B, N331DM, was substantially damaged when it impacted terrain during a forced landing near Dona Ana County at Santa Teresa Airport (5T6), Santa Teresa, New Mexico. The airline transport certificated flight instructor, and the private pilot receiving instruction were not injured. Visual meteorological conditions prevailed. No flight plan had been filed for the local instructional flight being conducted under the provisions of Title 14 CFR Part 91. The flight originated at 0808. According to the instructor, he was giving instruction to the private pilot who had recently purchased the airplane. They departed 5T6 with approximately 15 gallons of fuel. After completing four touch-and-go landings, they departed the pattern to do some air work, which included steep turns and a stall. At 3,500 feet agl, approximately 3 to 4 miles north of the airport, the engine lost all power. The instructor stated that he was unable to reach the airport using "best glide." The instructor made a forced landing in a field approximately 1/2 mile east-northeast of the approach end of runway 28. When the airplane impacted the ground, both the left and right main landing gear assemblies collapsed, the upper wing assembly was displaced aft, and the lower left wing, left horizontal stabilizer, and elevator were buckled. According to an airport employee, who gave the instructor and private pilot a ride back to the hanger, the instructor stated that the airplane's engine stalled and they had to land in the desert. The instructor also stated that he thought there may have been some water in the fuel. The private pilot asked the airport employee if he could borrow a vehicle to go back to the airplane to get their gear. The private pilot also asked the airport employee if he could purchase 5 gallons of fuel. According to the airport manager, the airport vehicle that the private pilot borrowed was equipped to use a special 100 octane Low Lead fuel that is color-coded red, instead of blue, to indicate it is for vehicle usage and not for aviation. At 0930, the private pilot purchased 5 gallons of 100 low-lead fuel. The fuel purchased, was logged as fuel for N331DM. The fuel was dispensed from the 100 Octane Low Lead aviation fuel tank, into a 5-gallon fuel can. According to an FAA inspector, on November 17, 2003, during a telephone conversation with the instructor, the instructor stated that he did not believe the owner had ever purchased fuel for the airplane. The FAA inspector informed the instructor that prior to selling the airplane, the previous owner fueled the airplane and then logged 0.7 hours of flight time and the instructor and private pilot had logged 0.8 hours of flight time. The airplane's records indicated a total of 1.5 hours of flight time since the airplane was last fueled. The instructor agreed that N331DM's fuel burn rate would be approximately 15 gallons per hour for a total of approximately 22.5 gallons, which was close to the airplane's useable fuel quantity of 23 gallons. The instructor was told of evidence indicating that the private pilot had purchased 5 gallons of fuel after the accident. The instructor stated that "he never goes into the desert without extra fuel." The instructor also stated that it took them a "couple of hours" to locate the airplane. According to an FAA inspector, on November 17, 2003, during a telephone conversation with the private pilot, the private pilot stated that he never purchased fuel for the airplane. The private pilot was told of evidence indicating that he had purchased 5 gallons of fuel after the accident. The private pilot stated that "he never saw where that fuel went." The private pilot stated that he thought the fuel was for the vehicle, but he never saw anyone put fuel into the vehicle. The private pilot also stated that he never saw anyone put fuel into the airplane, as "it sure as hell wasn't going to fly out of there." An FAA inspector, who examined the airplane, stated that there was approximately 4 inches of fuel remaining in the airplane's main fuel tank and no fuel in the wing tank. He also stated that the airplane's maintenance records were examined, and an engine test run was completed. There were no pre-impact deficiencies noted that would have precluded normal engine operation.