Personally I don't see how actual contact with aliens or their technology could be covered up, or kept secret, even if that was the doctrine of the day.
Let's not forget that the US couldn't even keep their nuclear projects a secret when first developed, and they ended up in the hands of their opponents. People are not robots, and human factors can never be eliminated entirely, with all the training and all the classification clearance in the world, and more.
When it comes to something as mind-blowingly monumental as actual proof of alien existence, I don't think any amount of top-secret classification could suppress that revelation. I just do not believe that it would be possible. I do not for one second believe that every individual within the intelligence community, or military, when presented with such evidence, would agree to play their individual part in suppressing that information. The ramifications of that knowledge would be so great as to break any loyalty to the chain of command or national security protocols. Enough people would want to share this with the world, and have the means to do so conclusively.
Again, the nukes. The Russians weren't just told about their existence. They didn't just give them blurry photos of a bomber. They leaked actual designs and testing data and yadda, yadda. Enough to build their own bombs.
I would say it is virtually guaranteed that the discovery of alien intelligence could not under any circumstances be kept secret.
Lastly, we have a huge amount of civilian equipment that could potentially detect alien craft in our atmosphere, or potentially even approaching our planet. It's hard to envisage a scenario where they get here completely undetected by civvies, only to buzz around posing candidly for the military. And then either crash for the lulz or leave completely undetected by civvies, again.
It's all far, far, far too convenient. Far too implausible. Almost any other potential explanation is exponentially more likely.