In my game, this question would be answered the same way the government answers a lot of questions,
"I'm sorry, that's classified."
However, vamping on what Harry has said throughout the books and particularly in Small Favor on walls, they wouldn't need to try to keep it a secret. The best thing about the modern world is that the public's belief in science is a self-maintaining anti-conspiracy theory.
Imagine you ask an MIB for an explanation and they say, "It's magic, Sir."
Now imagine you are an FBI agent....
Then a CIA Agent....
Then a Police Chief...
Then a Politician...
Then President Obama himself...
Their reactions will be identical to the Mailman on the 1st page of Storm Front.
First they laugh... then they ask for the Truth and all they get is, "It's magic, Sir..."
In my game, the few people in the government that do know would make like Karrin Murphy, keep the information to themselves. The few units put together to deal with the magical world would have to be motley crews most people think insane. Even a veteran Intelligence operative would be more likely to believe a convoluted Rube Goldberg styled assassination plot then an explanation of magic and the Nevernever.
In my games, I probably have one government position that's on the books, but not publicized called the White Staff, a liason between the White Council and the U.S. intelligence community.