The fact that it’s the US government isn’t the important bit; Armstrong isn’t asking you to trust the government, and his entire argument is explicit, no reading between the lines required.
What’s important is the “gigantic fraud involving 400,000 people” part -- clearly establishing that it would have had to be a pretty extreme effort. And rather than just saying “trust us”, he explicitly suggests asking people outside that group, such as scientists from other countries, who would be able to verify whether the moon landing was real.
And I completely agree with all of that. That doesn't change the fact that "the government wouldn't defraud you" is a horrific argument. And that is one of his points.
What’s important is the “gigantic fraud involving 400,000 people” part -- clearly establishing that it would have had to be a pretty extreme effort. And rather than just saying “trust us”, he explicitly suggests asking people outside that group, such as scientists from other countries, who would be able to verify whether the moon landing was real.