I agree. I posed it as a theory (hence the use of the word may). Coulson obviously has his reasons, otherwise he wouldn't keep his death a secret. We know Fury doesn't like to throw away his toys. He could have "shut it down" by giving it a skeleton security that would only respond to a certain call sign to be utilized when needed (like we've seen, so that would mean they shot SHIELD agents). That would explain how Hydra didn't know about it and how Coulson could have been the head of the department prior to its "closing", and then that memory was erased.