So I was curious and looked up "Independent Regulatory Agencies" as reference in the Executive Order.
They are:
the Board of Governors of the Federal Reserve System, the Commodity Futures Trading Commission, the Consumer Product Safety Commission, the Federal Communications Commission, the Federal Deposit Insurance Corporation, the Federal Energy Regulatory Commission, the Federal Housing Finance Agency, the Federal Maritime Commission, the Federal Trade Commission, the Interstate Commerce Commission, the Mine Enforcement Safety and Health Review Commission, the National Labor Relations Board, the Nuclear Regulatory Commission, the Occupational Safety and Health Review Commission, the Postal Regulatory Commission, the Securities and Exchange Commission, the Bureau of Consumer Financial Protection, the Office of Financial Research, Office of the Comptroller of the Currency, and any other similar agency designated by statute as a Federal independent regulatory agency or commission;
I was not willing to track all those authorizing bills down, so I looked at one, the Federal Maritime Commission, tracked it back to it's authorizing document (Presidential Order, Reorganization Plan number 7, 1961 as reference in 46 CFR 501.2(b) ) where it makes it clear that the Commission is an Executive agency and the "Independent " in the name is from other
Agencies not independent of the Executive. This despite the hyperventilating of news agencies.
I can only assume the others are similar, and fall under the preview of the Executive, and he's perfectly within his expressed powers to check their homework.
So in other words, the Media lied.