As an act of desperation, I will make one more guess. It's So Easy (1958) was the last single by Buddy Holly & The Crickets. Linda Ronstadt had a hit with the song in 1977. In January 1969, the Beatles sang a few lines of the song during a recording session for the Get Back/Let It Be album. (They also sang verses from All Shook Up, Don't Be Cruel, Blue Suede Shoes, Cathy's Clown, Be-Bop-A-Lula and many other American rock'n'roll hits.) Paul McCartney used to perform It's So Easy in concert and I'm guessing it was Paul, not John, who sang it during that recording session. But if it was John and if the snippet was used in a commercial, then I win!