You are completely incorrect....if they give it to him he can sidestep everything and declassified it. He is the ultimate classification authority. Period.
Actually, it is you who are incorrect. You are overlooking the part of your own statement that I put in bold above -- if they gave it to him.
We have three separate branches of the federal government: Legislative, Executive and Judicial. We have the doctrine of separation of powers. The Executive does not have plenary authority over the entire government, only of the third headed by the president.
The House of Representatives owns the document. It is their work product, written by a House committee chairman. So if the committee and/or full House votes to release the document, it can be released. Although there is some debate as to whether or not the document would then need to go to the White House for review, the President apparently has already said he would release it.