Subtext is more than just a layer. It's more like the filling between the layers. And it's not the easiest of concepts to understand. By definition, it's an underlying and often distinct theme in a piece of writing. It can be woven throughout the story, or the theme can merely decorate the work.
I'd rather have it woven through, but how the heck do you do that without beating the reader over the head?
I searched some more, because, frankly, I didn't know. Here's what I've found.