I understand that the melody for Dorogoj Dlinnoju is a traditional song and might predate the copyright from the Soviet Union. I don't think it matters much whether you borrow the melody from another song and put your own lyrics to it.
You can claim authorship of the lyrics. Not sure what Gene Raskin did here, but the tune was floating around prior to copyright date. It's a Russian Gypsy tune.

Gene and Francesca were a folkie act during the Sixties and he is a wonderful lyricist and parodist. He penned "A Personal Friend of the Tsar Was I" and the song "Kretchma" (after the famous New York Russian restaurant) That song was popularized by Theo Bikel. I've always been a fan of Gene and Francesca. They did a pretty version of "La Llorona", the famous Mexican folk song.

Every songwriter I know has taken the melody from some song or other and composed their own lyrics to it.   Woody, Dylan, McCartney, Harrison, ....plenty of pop songs based on PD tunes. I think in the realm of folk music, the tune is a vehicle for the words and is of less importance in its originality.

Now if someone were to claim authorship of a tune by Gershwin, Berlin, Porter, or Kern et. al. then that might be a little different. Many of those tunes were original and not PD.

My opinion of course.

Frank Hamilton