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I wouldn't say it's belief itself as much as "I want to believe" that aliens have either crashed here or made contact with us, but it's not anywhere like the major big coverups these conspiracies usually tell.

In my head-canon, these were otherwise minor incidents that only a handful of people know about, and they keep it under wraps because they don't know jack shit about the aliens, can't actually talk to them, and don't want to scare people as well as the evidence they have isn't conclusive because it's not made of fantastic magic materials, but just normal fucking shit you can find on Earth like gold and iron.

It sure would be more interesting than "it was a mylar weather balloon, and people just didn't know about mylar at the time and the only reason it even blew up was because of an over-zealous newspaper reporter who wrote that famous headline, while the retraction for that headline went completely under the radar as it was less sensational."