The difference is that to be against a country is to be against its people, while to be against a department is simply to wish it was run better. Indeed, sometimes the only way for a department to be run better is to outsource its functions to other departments – or into the private sector.
For example, if someone is an open critic of the EPA, believing it to do more harm than good, why wouldn’t those who agree appoint that person to run it, whether to change it or shut it down completely? It makes sense. On the other hand, one who actually hates society itself and its people, probably shouldn’t be handed the reigns of government. Those who criticize the EPA have a vision of a better American society without it. Those who are ashamed by the very community they belong to can have no better vision for that same community – only for a different one.
It’s not really the same thing.