That's the point: they are only the President of the Council of the EU, which is the (very) rough equivalent of the Senate; and pretending to be the Presidents of the EU reflects the Council's power grab. To give you the analogy, it's as if your Governors had taken over the Senate, and made the President and his cabinet yes-men for it.

_{*Lunatic*, n.
One whose delusions are out of fashion.}