No audio when importing AVI files into FCP

First off - yea, I know AVI was a format created by the ancient Egyptians and is now dead, however I have several I'm trying to incorporate into a friend's funeral video. The avi plays just fine in QuickTime Player but when I import it into FCP all I get is the video i.e. no audio. I've made sure Settings → Import → Remove Silent Channels is off. I know I can use HandBrake to convert it to mp4, but it recompresses as part of the process. I was hoping I could import it into FCP, clean up some poor lighting and then export it. Seems odd that QuickTime Player can handle it, but not the professional strength FCP :-/.