It's not so much an interpretation as just one aspect of the entire story. Go back to the first film when Morpheus says the Matrix is just a form of "control", and then laser focus on that word for the rest of the trilogy.

There are many aspects of the story, and while it's great to sit back and take it all in at once, it's also good to give it a watch through with a specific concept in mind.

I suppose in that way it's similar to what people find in their various bibles. Reading the same stories again and again, yet finding new perspectives and on them.