Jim, I did not want to be too specific, to avoid political discussions. Just some hints: my parents owned a book "Folk songs of Soviet peoples". Half of the content was openly communist. The other half was declared "heritage", but, as I was told later, consisted mostly of songs from the Soviet era as well, artificially aged.
Israel used to have an official authority which officially invented old Israeli folk dances and even Yiddish folk songs praising country life on Our Own Land.
For faked ethnicities, look at the Balkans. There must be many other examples, of which I do not know the details. -
If a song starts, say, "I've been a wild rover", nobody expects that the author or the singer is talking about her/himself. For the song to be "real", it suffices that it describes a reality familiar to the author from contemporary experience. That reality may well consist of a popular reception of an old story or myth, e.g. the birth of Jesus.
A song is definitely a fake if it pretends to be older than it is - the topic of this discussion.