There are too many dimensions to the idea of 'important' to answer the question directly. I think I know what you mean, and I tend to agree with you if you mean what I think you mean. I think. ;/
Of course history is important; if the facts of a thing are knowable they ought to be preserved and respected in some way.
But much of the impact a song has on a hearer is derived from outside the song itself, from the emotional and mythic resonance it brings along with it. And in many cases the popular, if mistaken, idea about the meaning of a song carries more emotional weight than the bare boring facts would.
So in that sense I think the myth may be more 'important' in the moment of experiencing a song than the fact. Nevertheless I still enjoy learning the truth about the background of songs when I can, even if it goes in the face of what most people assume it means.
-Glenn