That’s just overly simplistic thinking. I don’t believe the government or not believe the government. And I think in a situation such as this, the government would not have been able to keep it a secret. I think the government can keep some things secret. I evaluate each situation independently and don’t just decide ahead of time that the government is or isn’t telling the truth about something.
Also, someone referenced the Manhattan Project earlier as a testament to the government’s ability to keep a secret. But there is a huge difference between the two scenarios. The Manhattan project only needed to be kept secret until it was completed. If the moon landing were fake, it would had to have been kept secret for 50 years. Yet, there is still no proof it was faked. Additionally, the Earth is round. There is video of it. Lots of video.