Rok, while that's sound logic, I can give you examples when that is not the case.
"On Green Dolphin Street" is composed by Bronislaw Kaper, but his version is most certainly not my favorite.
[url]https://www.youtube.com/watch?v=WY1wvhjZ00I[/url]
That comes closest to his version, with him playing the piano, but I can't find that one.
Here's the same tune by Miles;
[url]https://www.youtube.com/watch?v=xGVdAlxlp18[/url]
Which do you like best?