In some cases it might be advantageous to have an outside objective view of a culture. I think of probably one of the greatest interpreters of Italian classical songs, Jussi Boerling who was Swedish.

Pete never tried to adopt the musical characteristics that were specific to cultural styles, though. He did it his way.

Leadbelly sang songs his way and changed them (ie: Kisses Sweeter Than Wine taken from Dhrinnan the Cow, an Irish song.

I think that jazz is a product of musical acculturation.

Most folk music is the same. You can slavishly try to imitate another singer or in attempting to play so-called "alien" music, you might define your own style.

The most problem you will have with this approach is that there will always be stuffy academics who will say "that's not the way you do it." It's best to ignore them, folk snobs and pseudo musicologists.

The most important aspect in performing music from another culture is to
try to understand it in depth as best you can. Even in the traditional cultures,
the way some play the music in one village will differ than the way some do in another village. The idea of authenticity becomes vague; the attempt to approach it sincerely and study it gives the performance a validity of its own.

Take the blues for instance. In spite of the attempt, many white blues artists don't have quite the same phrasing or physical interpretations as black artists but so what? They study and what they do is valid in expressing the meaning of the music rather than an arbitrary "style".