Is Armageddon based on a true story?

No, the movie Armageddon is not based on a true story. If a comet had really come that close to hitting Earth, but been thwarted by a bunch of astronauts, you wouldn't have to ask this question. You would have heard about it already.

It's important to remember that exciting stuff like huge disasters, or gruesome murders, or monsters would be front-page news in every newspaper and on every TV channel.

When wondering if a movie is based on a true story, you need to first ask yourself, "How likely is it that something like this could have happened, but I missed every single news report about it?" Usually, such a thing is not very likely.

If someone found proof that Bigfoot existed, or if the Cloverfield monster was actually found in the ocean, or if a chainsaw-wielding murderer killed dozens of people in Texas, or if an asteroid almost hit the Earth, you would have heard about it LONG before the movie came out.