There have been two "shootouts" between American Forces and greys. One has been corroborated by two whistleblowers, the other by one.
The first reportedly occurred at a joint human-grey facility at Dulce, New Mexico. It was seen firsthand by Phil Schneider and knew about by Colonel "X" who published his DD-214 in the book "UFO Highway" with his name blurred out. Phil Schneider possessed severe wounds, including missing fingers on his left hand and a huge scar going down his abdomen, which adds a degree of credibility to his story. The conflict occurred due to scientists entering a level of the facility reserved for greys. Phil got involved because he was working on an expansion to the facility and had roped down a hole into a tunnel where both sides we're actively shooting at each other. A grey shot at Phil, severely injuring him. Phil said a SF soldier jumped between Phil and the grey, absorbing most of the blast, dying in the process. There were 68 human casualties.