Last I heard, this covert group, also called Majestic 12, is not a part of the government anymore. They were until 1969, after that, they became a
private owned organization, financed by big money (coming from unknown sources). So, it may be very possible that the government can't say anything -
they simply don't even know. Maybe MJ-12, when they were a part of the government, had too little information or the president at the time decided to
shut the group down (either MJ-12 wanted to be a private organization, or something else).
Why keep it a secret then? Well, the first thing is of couse: people would panic. Second, I think the high-ups want it to be a secret, in case the
aliens would be friendly or scientific. That is, imagine if the public knew there were aliens out there, and that they were peaceful. Corporations
don't want this. They don't want peace, because with peace, they can't gain anything. The aliens would learn people new stuff, maybe new systems of
government, much better than ours are now. That would be catastrophic.
And if they come, in the near future (2012

), evil or good, is there any sence why they would keep it a secret? Well, they could develop a plan,
maybe they have constructed secret bunkers and all, or are constructing. Might as well use the system as much as possible to get as much as possible
to survive in those bunkers, as long as possible. Yes, when a life-form faces desperation, it will most likely use any method to survive.
Or, the last option. There are no secrets, no aliens or UFOs in any group's possesion. Therefore, nothing will be revealed because there is nothing
to reveal.