Do you know for sure how that "real thing" learned the song?
As far as I know, they learnt them from their parents and grandparents and uncles and aunts and friends and neighbours. It's called "The Oral Tradition".
If the grandchildren are now learning songs that Brasser wrote down, is that any different from them going to a library and finding a song from another collection?
Yes, because they grew up hearing their parents and grandfather singing them. It's called "The Oral Tradition".