I doubt ASCAP or BMI will be knocking on anyone's door since the Greenwood song was a second generation element and not the purpose of the video. Now, if someone had been singing the Mickey Mouse Club song, Disney would be hacking heads.
Another question comes to mind. Hypothetically, what if a copyright holder simply didn't wish to have his song associated with a particular event, and refused permission for that reason? Does he have the right to control who can use his property in that circumstance?