That's an irrelevant distinction. Neither are part of the judicial branch, which is the relevant consideration here.

Consider: Congress passes a law which sets limits on the authority of an agency. You think the agency itself should get to decide what that law actually means? And the courts, the branch of government specifically granted the role of arbiter by our constitution, should be required to differ to that interpretation if anyone ever objects and brings a lawsuit? It's absurd, and no less so than if the law was concerning a private company rather than a public agency.