The realization that we are alone would probably also be withheld from the public as governments tend to think of themselves as somehow superior.
Here's the thing though:. You always have rogues in there somewhere. If we had discovered aliens someone would have found a way to disclose it. Realizing we are alone is harder though. People, even very bright people, will grasp at straws forever. This is demonstrated every day by the existence of so many endeavors people take on that are the proverbial needle in a haystack. It can lead one to ignore the obvious.
The ultimate destiny of the human race has yet to be determined but the proper direction is relatively clear. It begins in realizing that we, as a species, are clearly alone and that we, as individuals, are not going anywhere beyond our immediate neighborhood. And we need to be ok with that because it is ok.
Once these realizations are truly made we can indeed move on to initiate the fulfillment this destiny. Or we can put the future of our place in the universe at risk by diddling around looking for non-existent aliens and fooling ourselves into thinking that putting humans into space on a mass scale will ever make any sense when clearly it won't. It's our choice.