At the emergency services debrief for the Kegworth (M1) crash in 1989, I understand a senior police officer asked who was responsible for sending the military SAR helicopter that landed on the motorway unannounced about an hour into the rescue operation, frightening the hell out of everyone on the ground.
A few years later, at a disaster plan coordination exercise for the Southend Airshow, (scenario; Red Arrows opposition pair collide, one aircraft dives into large crowd on sea front, the other crashes into the sea with pilot ejecting) I heard the RAF SAR representative, when asked what action the nearest RAF SAR unit would take, tell the stunned meeting that the Seaking crew would search for the missing pilot!