No, I didn't misunderstand anything you said. You think that, because you believe that the President has full authority over all employees of the executive branch, which he only thru the heads of those departments, EXCEPT for the DOJ IG. If you believe otherwise, I urge you to research 1978, post-Watergate insurgence , where Congress gave them extraordinary functional independence within the executive branch and made them more beholden to Congress, and not the President.
Hard to claim something unconstitutional that isn't backed up by the constitution or has language that supports such a claim. You are trying to argue opinion (yours) and not facts.