GarageBand 3: No Audio error when importing movie

When importing movies, GarageBand sometimes displays a QuickTime alert message indicating there is no audio.

"The QuickTime movie "movie_name.mov" does not contain audio that GarageBand can play. The movie will be imported with no audio."

This dialog either means that there is no audio track in the movie file, or that the movie is an MPEG1 file in which the audio is muxed into the video track and therefore can't be extracted.