I'm not sure its just faulty memory. I don't know that people strive that hard to reproduce a tune or song that slavishly.
I find that the melody of a song or tune is intimately linked with the shades of meaning - similar to expressing spoken words with different stresses and different rising and falling intonation. So that the source representation (whether read or heard) I'm working from is more of a starting point than a set pattern. I dislike the idea of being constrained to a particular pattern - I would rather absorb and understand the pattern and then perhaps reinterpret that idea & work with it. Modernisation is only an extension of this surely?
That seems to me to be more the folk process - successive people reinterpreting and playing with the pattern/ideas, rather than a pattern imperfectly recalled.

Kris