Yes.

Very possible if the boat was moving along at a decent clip, anchor grabs suddenly....[Bleeeeep!]-end is yanked down. TedR describes the physics of it all pretty well.

Very poor judgement and/or lack of experience displayed by the people in the boat. They are indeed lucky to be alive and I'm glad no one got hurt.

Still a good reason to keep a sharp knife at the ready, arm's length away or less from your rope.