If there are no aliens, then I wondered, how could such a vast conspiracy start and be maintained? Initially, I was stumped. Then I had a flash of insight.
Our world has had a history of mass hysteria. Perhaps the most famous instance involved an imagined attack by aliens, induced by Orsen Wells' radio broadcast of War of the Worlds.
Imagine something like that occurring today, maybe due to an invention, like secret hologram or aircraft tech. The people would go running to the government to save them. The government would say there are no aliens. However, many people would accuse the government of a cover-up. Riots might ensue. Revolution might be in the air.
The President might realize that he has no choice. He has to give the people what they demand. So he goes on the air to admit there are aliens (even though there are none). The President would call for Homeland Security to protect the people from the "aliens". The people would beg to be interned in FEMA camps, which grow to become exclusion zones.
That gets us close to the show's situation. We just need a few years of building walls. And a way to fake that spaceship.
Why doesn't someone in the know leak the truth? Well, in my hypothetical scenario, the government tried telling the truth to start with. That almost had caused a revolution. It's not going to be any better telling the people the truth after the government has treated them as cattle. The truth could result in the collapse of society and the deaths of millions, starting with the bureaucrats. The bureaucrats would decide it's better for everyone if they just keep their mouths shut, while enjoying model-stocked parties in huge mansions. It's a dirty job, but somebody has to do it.