What was shown on TV was not real.

I agree.

If something had gone wrong, it would forever tarnish the USA's reputation and prop up the Soviet Union in the grand pissing contest of the Cold War.

So, sure...

Land on the Moon and send just enough of the real footage to the Ruskies so they know we actually did it.

Then, televise a censored, edited, or outright mock copy of the original to show "live" just so it looks like astronauts are competent to the nth degree.

If the Ruskies deny the fake televised version, then air footage that indirectly supports the "live" version to shut them up.

Besides, we'd never been to the Moon. What if Armstrong stepped foot on the surface and immediately his suit was torn apart by acidic soil and then he popped like a pimple as his suit imploded?

There's no chance I'd air the landing live if I were in charge. Just thinking logically, it would be like putting Biden on stage without a teleprompter. You're just asking for a disaster.