Just to build on the even cover tunes should bear the stamp of the musicians playing them theme, I have a running dispute with one of my guitarists about this. He rarely can tell exactly what made the original sound the way it did, but picks and demands that others add specific, generally small touches he has been able to hear in the original. Then, when the result is not like the original (no one is surprised at this but him), he accuses the person he asked to make a change of not trying to get it right.
Fortunately, he doesn't do this constantly (Only during certain phases of the moon?). But when he gets picky with me, I sit him down and explain that many times I do not want to play exactly the way the original player recorded the bass. Not (well, usually not) because I disrespect the player on the record, but because I want to challenge myself to come up with something of my own (even if it's not as good, at least it's mine). This does not mean I don't often practice original lines for the learning, but if my goal was just to hear the original lines for everything, it'd be easier and cheaper to invest in a better stereo...
Unfortunately, he, like some people, really can't understand why I don't consider doing it exactly like the guy on the record is not the end of my aspirations. Believe me, the guy has other redeeming features, but this issue is really frustrating!