Art of Interpretation

I remember very well when I first saw a music video for the song "Nothing compares to you" (Sinead O'Connor) on TV. At that time, I studied French at a secondary school and didn't know a word in English. But the song title had been fortunately translated into Russian which led me to think that the song was about ... God. In spite of the fact that I grew up in a family of communists and atheists, and God was not mentioned in my home at all. So, I'd been sure that this song was about God until my student years when my mates whose first foreign language was English laughed to scorn my subaudition. They explained to me that the song was about a love break and parting. Nevertheless, every time I hear it my feeling remains the same and I wonder if native speakers might understand this song in such a way, at least in theory?