The guy who wrote a song can play it any way he wants.
A band covering a version of a song has a clear road map (a recording) of what to play.
Play it that way or not.
Might as well just stay home listening to the record, then....
'sides... which version of a song is the authoritative one? The version of Closer to The Heart from the original record or the one from Different Stages?
N.b the purpose of some bands, e.g. jazz bands, jam bands, bluegrass, etc., is intentionally NOT to play everything just like the record.
