What do Dave Allen and Paul Daniels have in common?

From the BBC:

Paul Daniels, 73, lost his left index finger and the tip of his ring finger in an accident with a circular saw while building props for his act. He drove himself from his Berkshire home to hospital in Henley-on-Thames, where the index finger was reattached. He told BBC Radio 5 Live: "I've only lost the tip of one finger. It could have been a hell of a sight worse."

What a trooper! Didn't even call an ambulance. Or maybe he did, but then remembered that it might take it four hours to arrive and six hours to get back.

Two explanations of how Dave Allen lost a finger are here, both seem equally plausible or implausible.