Are Bert and Ernie named after characters from It's a Wonderful Life?

It's been stated in numerous articles, websites and television shows that Bert and Ernie were named after the policeman and cab driver from the film It's a Wonderful Life, who were also named Bert and Ernie.

There has never been any official confirmation of this statement, and most sources from the Henson company have said it to be merely a coincidence.