The thing here is, we'd be dealing with aliens, not with the atomic bomb nor satellites. Hiding alien-related technology/knowledge would be an even bigger issue. Those who would be working on it would know very well that they aren't doing it just "to protect national security", and the bigger the secret, the harder to keep it. Technology knowledge is constantly being stolen and sold; if you remember they could only keep the details to build an atomic bomb for no more than four freaking years (which is when the Soviets tested their first one after having stolen a whole lot of information from the Americans) then you should also assume a lot of other governments would have already stolen that other info we're all looking for. I highly doubt that, if the Roswell Incident involved aliens, nobody has stolen any information about it after sixty four years! Sixty four! Not just four...
And, again, if they secretly keep any alien bodies and technology, then they are wasting all of their money in something that doesn't have any use. Because, after all, satellites and bombs have been used in warfare... but have you seen any alien technology around? What's the purpose to hide such things if you never use them, and nobody else can use them either?
That's what I, personally, would find to make any sense: that nobody knows how to use what they found. Then, they'd be forced to let more people in just to see who can make something out of it, because if they don't, they are losing money they could be investing in other useful projects. But in that case, the staff would be so big that the secret couldn't be kept. It's just impossible.
According to the logic of many people in this forum, I can fly and Mischa Barton is secretly in love with me just because I dreamed of it.