but statistically they probably exist

What statistics? We haven't found all the variables of the Drake equation yet. We might be alone in the observable universe.

Oh yeah, this has happened multiple times, and the story is always the same:

1. The government says they're going to release info on UFOs. This caused a brief flury of interest from the general public which is reinforced by the conspiracy theorists who swear that this will finally be proof of little green men at area 51, or whatever.
2. The government takes a while to follow through, during which time the general public slowly loses interest. The conspiracy theorists start getting impatient and publicly worrying that there must be a faction within the government that's deliberately slow walking the release or even modifying the documents because they don't want The Truth to get out.
3. The documents are finally released. They consist of 99% dry, beauracratic paperwork and 0% admissions that aliens have every visited earth, but the conspiracy theorists dig through and pull out a few scraps that can be spun to make a good headline.
4. The nation spends at most a week talking about "video taken out the window of a fighter jet of a mysterious floating orb thats porobably just a balloon" #27, or "eye witness account from a sleep deprived 18 year old soldier who swears he saw an alien space ship while on guard duty at 2am" #382.
5. The national news cycle moves on, and most people promptly forget about the whole thing. Meanwhile, the conspiracy theorists take whatever scraps they were able to find and add these to their rotating library of bullshit to talk about. The initial promise that this was going to be irrefutable proof that aliens have visited earth is quietly forgotten. If it ever does come up, they blame that shadowy faction of the government which must have succeeded in watering down the release before publishing it.

Rinse and repeat.