A song "means" at least three things:

What the writer (and composer, if there is one) meant.

What you want it to mean.

What you're afraid somebody else will think it means. (This last kind if meaning got traction, I believe, only in the PC era.)

For most purposes, what a song means is a rational inference from what it says and sounds like.

Traditional songs, what with forgetting and modifying, can sometimes be fairly ambiguous.

You may "appreciate" a song better if you have the lowdown on the songwriter, but it seems to me that the most important meaning is the one that comes through most clearly in performance.