Perfect, but a problem. Had the ringtone been a common telephone ring, the scene could have dropped into the final edit without a hitch, the moment providing a quick bit of emotional texture to the film. But EMI Music Publishing, which owns the rights to "Gonna Fly Now," was asking the first-time producer for $10,000 to use those six seconds. (Times)
I don't know how to state the distinction, but it's obvious: the documentarian was not using this song to enhance their documentary, they were recording an event in which the song incidentally appeared. Recording this event should be no more a copyright violation than the woman playing the song in the first place is one.