Heard it was an A-4 in El Toro... and he ended up with an electrical power failure in the process or something...
Lots of urban legends have some grounding in reality; this might be the genesis of where this one came from:
Air Incursions and Attempted Air Incursions
Robert K. Preston (February 1974). On February 17, 1974, Robert Preston, a private in the Army, stole an Army helicopter from Fort Meade, Maryland, and flew it to the White House Complex. He passed over the Executive Mansion and then returned to the south grounds, where he hovered for about 6 minutes and touched down briefly approximately 150 feet from the West Wing. Members of the EPS did not know who was piloting the aircraft and were not aware that it had been stolen from Fort Meade. They made no attempt to shoot down the helicopter.
Preston left the area of the White House and flew the helicopter back toward Fort Meade. He was chased by two Maryland State Police helicopters, one of which he forced down through his erratic maneuvers. Preston then returned to the White House Complex. As he lowered himself to about 30 feet above the south grounds, EPS officers barraged the helicopter with shotgun and submachine gunfire. Preston immediately set the riddled aircraft down. He was injured slightly.
[FAS Note: In response to the preceding paragraphs, the following first-person account of the Preston incident was provided by Maryland State Police First Sergeant (ret.) Louis W. Saffran and inserted here by FAS:]
The Maryland State Police Helicopter was not with the Stolen Helicopter when it first flew over the White House. The State Police Helicopter responded after being notified by Andrews AFB Tower that there was a problem with a rogue Helicopter in the area of BWI Airport. The Crew of the State Police Helicopter responded to BWI Airport and chased the rogue Helicopter down the Baltimore/Washington Parkway (I-295) into the restricted area of D.C. After a brief dog fight around the Washington Monument, the rogue Helicopter flew toward the White House, over the fence and on to the White House lawn. It was at this time that the Maryland State Police Helicopter took a position between the rogue Helicopter and the White House in an attempt to keep the Rogue Helicopter from harming the White House. It was at this time that the Secret Service fired on the Rogue Helicopter, forcing it to the ground. Robert Preston, pilot of the rogue Helicopter, exited the aircraft and ran toward the White House. I exited the State Police Helicopter, and along with the Secret Service Officers, subdued Preston after a short foot chase.
This escapade was documented in the Congressional Record, Per Senator Goodloe Byron, and in many newspaper articles throughout the United States. The facts of this incident were provided to then-President Richard Nixon who called Trooper Donald Sewell and me to the Oval Office later that week for a Presidential Commendation.
At no time was a Maryland State Police Helicopter forced down by the rogue Helicopter. The State Police were instrumental in the downing and capture of the rogue aircraft and its Pilot on the White House Lawn.
http://www.fas.org/irp/agency/ustreas/usss/t1pubrpt.html