The song has virtually nothing to do with the Smith case.
Lyrics here.
The Smith case involves a group of men who are all claiming paternity. That's just the opposite of the situation described in the song, in which a man denies paternity and a woman insists that he's her child's father.
But I see that there's a link on that page to an Anna Nicole story, which means that the people at Astra Labs, the host, have an interest in tabloid current events. I don't make much of that. There're also links to "Christian Baby Gifts" and "Barrel Chairs Factory" on the page.