Interesting thread. I guess many of us haven't really thought about how we honour tradition (please excuse the UK spelling!)
I will base what I do on what I hear from a live or recorded performance, or maybe on a printed source of music/songs. But I won't slavishly try to imitate someone else's performance, even if I might admire it and think their version is insurpassable.
I might change it to suit myself, perhaps sing in a different key because my vocal range doesn't match the original performer, and I might even arrange it (if accompanied) differently, again to suit myself (maybe I'm not capable of playing it the same way as the originator). But of course with tunes I will stick to the original tune and not attempt to change it, I'm just talking about the arrangement.
I might unconsciously change a tune or even words, without realising I'm doing it.
Not sure if I'm missing the point here - a lot of this could apply equally to comtemporary material as well as 'traditional'. (Have I missed the point? Please say if you think I have).