Jan, it's an excellent topic. There are times when I think the reviews ask for story that is completely outside the intended scope or message of the song. They are asking, in effect, for a different song.
But there are other times when the song screams for more 'story'
We need to get our story straight. What do we mean by 'story'? Basically it means "who, what, when, where, and / or why?"
But beyond this, it has two subtly different meanings. One is for the physical facts to be laid out more clearly. This is the request that sometimes grates on the lyricist, who has no intentions of rewriting his lyric to satisfy a reviewers random request.
But the other kind of story is the fulfillment of the one the lyricist set out to tell. The elements of a song have to be self-supporting. Who decides? A consensus of listeners. Since we don't have that level of access and communicaiton with a large body of listeners, we rely on reviewers.
With regard to love songs as you mentioned, when writing directly 'to' your love, sometimes a lyric just doesn't connect because it is goes TOO FAR in speaking directly. If you were really speaking to your love or ex-love or whomever, it's a fair assumption that the person would know what you were talking about - your shared background, etc., so you would never need to address it. The only thing that is important is your message, which in your mind, shines against the backdrop. But your audience lacks that context and cannot see the backdrop in your mind. You may think your lyric conjures it up, but perhaps it is insufficient. So in that type of lyric, you need to 'step back from the topic', because you are too close, and fill in enough context or story so that we know enough to relate to your words. In this type of lyric, the context becomes the story. When context is lacking, we can't relate well enough to your words to get their full emotional impact (which is what we are going for in songs) so we ask you to fill in the details of the story. It doesn't have to be the who, what, why, when, where details. It doesn't have to blow the mystery. It just has to set it up better, so you can knock us down better.
You might feel that you are 'fudging' on the integrity of the lyric to include context for the listener, that you wouldn't if you were really talking to your lover. It's partly a matter of how skillfully you do it. And it's partly a matter of remembering that songs are art, not real life. Making art more life-like does not necessarily make for better art. Understanding your medium, including its limits, is what makes for better art, better songs.
Your posted lyric, I CAN'T STOP LOVING YOU, for example, does a fine job of telling the story. It gives us all the context we need to appreciate your words. Nicely done.
Norm