Tv licensing is usually the same as movies. In your example they would need to reach an agreement with the publisher of the song--but it seems as if they recorded their own version on violin.
Where tv is (or used to be) different is that some tv shows (especially variety shows) would use a networks blanket license with ASCAP and BMI for a song that was performed on the show, which created problems with dvd releases as all the songs had to be re-licensed (since they were made under a contract that didn't anticipate many future rights). This also was the case with many tv shows that used songs in the background or as a soundtrack, but made dvd releases very expensive (or near impossible) as they had to re-license both the publishing and the specific master recording used. See attached article.