The myth seems to have been started by the English food writer, Jane Grigson in her 1973 publication, Fish Book. The exact quote is: "Throw away any mussels that refuse to open."
Nick Ruello is a mussel expert and fisheries biologist and he was commissioned to write a report for Seafood Services Australia, on the rather specific topic of adding value to mussels. Along the way, he cooked and ate over 30 batches of mussels, of various sizes, ranging from 21 to 111 mussels.
Nick Ruello found he found that some 11.5 per cent of mussels remained closed after a so-called "normal" cooking time. When he forced them open with a knife, every single one was both adequately cooked and safe to eat.
http://www.abc.net.au/science/articles/2008/10/29/2404364.htm