The punk icons were invited to make a comeback at the star-studded launch of the sporting showpiece, but declined the offer.
Former bassist Glen Matlock has now revealed their decision was made after they heard about Olympic bosses' major blunder in inviting The Who to perform with their late drummer.
He told the Daily Mirror newspaper: "I heard that they wanted The Who to do it, they wanted Keith Moon to perform.
"But he's only been dead 20 years.
"They had asked us to perform but the story about Keith Moon and The Who didn't help their pitch to us. That was one of the reasons we said no."
Moon died from an overdose of prescription drugs in 1978 at the age of 32.