John, I could imagine they left it out on the LP in order not to give the song too much popularity without the context of the scene in the film.
I've thought about your question since, and could also imagine that the similarity of the tunes is no coincidence. Maybe it was MEANT to demonstrate the Nazis' unscrupulous use of German traditions and cultural achievements to further their aims.
As to the Lorelei song: The Nazis realised its popularity and didn't try to suppress it. They simply printed it in song collections identified as 'trad'. There are still Germans who believe to this day the author is unknown. - Susanne