If you own the media then you can sit back and relax. At most you'll get few days of moaning and things will go back to normal. Majority of people won't even know or connect things anyway.
If media are licensed, then they will never run anything that will upset government too much. I've seen this many times. Even if hostile nation's media pick up the topic and report it honestly, the government can dismiss it as a conspiracy theory or just say it is an attack.
Ultimately even if people see all the evidence, most of the time they'll pretend they didn't and stick with the status quo.
Things are obviously more complex than everybody just automatically not believing, and owning the discourse makes all the difference (although owning the press like a sibling comment says is overkill). But it happens again and again on politics, and rarely becomes a problem.