I'm not sure that you can suggest that something "as sung by" qualifies as folk although it may qualify as popular. Handel's Messiah is popular but it is not folk. A necessary aspect of a folk song is that it can be sung by anyone, it loses it association with a person and becomes whatever the singer at the moment wants it to be. A lot of the songs that are popular now may be folk songs in the future, near or distant, but not until the writer, singer, or band that brought them into fame becomes less important than the song itself.