Inspector Generals are very similar to FBI agents in their qualifications. They carry firearms, too. They operate independently and are appointed either by the president or the secretaries of the cabinet. The appointments by the president have to be approved by US Senate.
Council of the Inspectors General on Integrity and Efficiency (CIGIE) (click here)
The Council of Inspector Generals on Integrity and Efficiency was formed as an interim between the direct powers of the president and the Inspector Generals. I do not believe the Inspector Generals are an exact fit into the Executive Branch and the president does not have direct authority over the WORK of the inspector generals so much as appointments of some.
Signing Statement to "Workers First." (click here)
The Inspector Generals stand the line between corrupt, corruptible and honest government. The hiring and firing of IGs are within the powers of the president, however, all these activities have to be reported to Congress. In that understanding is the balance to "honest government."
If Donald J. Trump manipulated the oversight of the new IG to allow $500 billion to go unchecked to the financial markets he would be in violation of the law that clearly states there would be oversight through these standard mechanisms. The public would then be aware of his antics.