However, as opposed to modern day anthropologists, all those German writers didn't exactly "collect", as in, hunt down songs and stories and transcribe them. It would be more accurately to say that a great many of them tried their hands and, well, writing their own.

I've been told by a lit scholar friend that Alexander Pushkin in Russia did both - as in, genuinely transcribed songs (as a Russian nobleman he was a bit more used to contact with actual peasants, I guess) and then, sending the collected materials to an anthropologist friend, added in a letter "BTW, I loved this so much I tried writing some, so six songs in this collection are mine, guess which". Nobody still knows which.