Not just copyright law. Look at the difference in laws being recording a video of a person and recording sound of the same person. I would love for law to be consistent, but as of yet there is no such requirement.
Another fun legal question is what happens if I add fake audio to a video where the video is legal but the audio isn't, but I use legal audio recordings to fake the voice of the person I videotaped? Does it matter if the injected audio is close enough to what was originally said (say I remembered the words while I recorded the video)?