Here are some examples that make me give the idea a little credence -
To this day, despite over 1000 years of Christianity, Russian people continue to uphold some superstitions (and, in the case of 'Maslenitsa'[1], holidays) that trace their origin to pagan pre-Kievan Rus'. Strange phenomenons that never found an adoption by the Orthodox church, e.g. that each house possesses its own spirit ('Domovoy'[2]), and that you best remember him and ask for good luck and protection when you leave for a long trip by looking in the mirror and sitting still, in silence, for a few minutes right before you depart. Fail to do so and you have no one to blame but yourself when you return to find it burglarized..! (Or so my immediate family sternly lectured me)
Actually, here we have a fairly ancient holiday, too - Valentine's day's origin can trace itself to when the Romans decided to rebrand the fertility festival Lupercalia, keeping the message (a day devoted to romance) the same, but putting a stop to revelers beating each other with skinned dogs and copulating in the streets.[3]
My point is that while we may forget why we do certain rituals or superstitions, our cultural memes are often imprinted onto us for hundreds of years or more (think weddings!), provided that our culture has descendants to carry the tales. So this makes Bastide and Fabbri's idea not so outlandish. However, it's very difficult to control what cultural memes stick and which ones die - sometimes, it's pure randomness. I guess these folks were betting on the slim chance of the song being so ludicrous and catchy, that it will just have to be told over and over for generations...
[1] https://en.wikipedia.org/wiki/Maslenitsa
[2] https://en.wikipedia.org/wiki/Domovoy
[3] https://www.history.com/topics/ancient-rome/lupercalia