I think your analogy is reasonable to a point, although corporations and governments are very different. To continue it, is the president going to be forthright to the public about climate change, if the EPA is no longer allowed to issue its own press releases?
Edit: Sorry, these agencies are not the only two that have received gag orders: https://sunlightfoundation.com/list-of-federal-government-ag...
Still, it's not every executive agency.