I know others have brought this up, but I find it very hard to believe that any single government would be capable of covering up such a large "happening", much less several or many governments. It's much easier to believe that such beings can exist than any gov't is capable of covering up their existence for as long as they supposedly have.
Let's look at that for a second, especially after the signature of the first atomic weapons was sent (incidentally) into space. That defines a level of scientific development beyond the ordinary (what we know as Newtonian) phyaics, and possible a civilization on its way to either the stars or self-destruction (or even both).
If I happened to be a sentient species on a distant planet, noting the 'disturbance in the force', if you will, having the ability to travel galactic distances, and thus the ability to discern planets capable of producing and even containing life, that would narrow down the search area, and who to check on ever few hundred or thousand Earth years. However, once the transition had been made form what we know as Newtonian physics to Einsteinian physics, the interest level would go up. Earth orbit capability and programs as 'primitive' as the V-2 would signal an interest in exploring off planet, so the interest level would go up considerable.
An old medical book I got from the late 40s fully anticipated nuclear war. Oddly enough, there was an entire section pasted into the back as an appendix dealing with that topic. It didn't happen. Humans are still warlike critters, the Nuclear Winter hadn't been proposed, there was still plenty to fight over, and another generation coming of age, yer we confined out hostilities to snoop and poop operations, threats, and proxy wars, with the occasional saber rattling of an impressive 'test'.
About the same time though, we started seeing things in the skies, perhaps out of piqued interest, but in increasing numbers, apparently interested in our use of atomics, our military capabilities, bovine anatomy, and eventually, the 'probe'. If those were not a hoax, we were indeed being studied...
Our transmissions, plenty enough would be monitored, translated, in an effort to understand our culture and motivation, and our leaders would be figured out in short order. It would be little enough to drop in at Camp David or any other remote location which was under guard, and interact with the people there. As a leader, I know I would want to meet with the visitor to discern as much as I could about them and their culture and their motives, and perhaps, just perhaps, obtain some sort of unfair advantage for my country, my 'tribe'.
As would the leader of any other country with major capabilities.
Nor would I want those meetings made known. Not to my people who might have a serious misunderstanding about the nature of those communications, nor would I want my enemies to know, because there is a good chance they would want to do all in their power to devastate my country before I could capitalize on any advantage I might be able to gain.
I am a firm believer in American exceptionalism, mind you, because I believe we have (had, anyway) a system of government that nurtures innovation, that rewards performance, that incentivizes the idea of developing the next gee whiz gadget and being the leader in all we do. We are a highly competitive race, after all. As were our main competitors, though their governmental form limited the ability to capitalize on that desire to compete, sometimes to hairy chested lady shotputters, or to stolen plans for the last innovation or copying things, but they, too, had firsts we cannot ignore, from sputnik to the mig 15.
Just perhaps, a few bits here and there were let out to see what either of us would do with them, with the promise of more little breakthroughs in exchange for not destroying each other, and for generally making the use of such gadgets as the one on which I am typing this commonplace. Even this relatively primitive box would have been a huge advance over the computers my father worked on when I was a child.
It would have been beyond 'gee whiz'. A cell phone would have prompted reverse engineering programs that might have taken decades to ferret out the workings and not only replicate them, but adapt our culture from the party line dial phones of my youth to the idea of having more computing power in your pocket than I have even on this computer (less storage, but more processor), and a screen with resolution to fit this missive on a postage stamp.
Did we do this by ourselves? I'd like to think so. But there is that alternate explanation, that we had help at some level. Would the governments keep it secret? Would it get out of the gulag? Would Americans believe it? Between national security and ridicule and the threat of professional destruction, most folks would indeed keep quiet and the remainder could be marginalized. The governments would keep the secret from their people as long as they could, and certainly from other governments for as long as possible.
And if the secret hadn't been kept, those who spoke up are questioned, because we wouldn't think the secret could have been kept, when, if there is a secret to keep, it hasn't been. Suppose, for a second, that all those 'top secret leaked reports' were true. What if it had been released and no one believed?