First of all, it doesn't have to be just a merely subset of cultural studies. We can theoretically assume for now that the set theory allows for having a common part.
That would mean there are some parts that both have in common but at the same time there are parts that differ from each other or at least are independent. Is that justified? We cannot escape from the cultural aspect when talking about literature. This does not come only to theory but also to other fields - like history e.g. Literature is a product of an entity entangled in their culture. Everything that happens in literature is a given cultural mirror. We cannot create anything in isolation from the world we know and live in. The same goes with some theoretical concepts - especially today when many conceptions mingle with each other and seem to have impact on theoretical contructs (like gender studies e.g.). But at the same time there might be some aspects that do not really bother with cultural studies.
Can we talk e.g. about semiotics without knowing anything about our culture? Can we talk about semiotics without knowing anything about literature. Nope. Maybe. 914
But this is something really not clear enough. Anyway that understanding would be impoverished. At the same time, literature can exist in its own world and would not be necessarily interested in taking part in any clearly visible social discussion as it is enough for literature to tell a story of one individual being entangled in their inner and outer world.
So it also comes down to the inner world placement. This is just a huge field of interconnections as I see it and I think this can be the reason for your confusion.
I find the part about origins pretty simple. First, people started creating. All the reflections about their works came much later. So at first only literary pieces in isolation were analysed and probably no cultural impact was taken in consideration at that point. But then it started to go deeper and deeper. Basically a view that literature theory is cultural studies is a product of... cultural studies. If we change our point of observation there might be no culture at all but the very piece of literature only. Our cultural conscioussness today however tells us that might not always be the thing.
Not sure if that helps you anyhow :) 914