Earlier quoted context omitted.
Realistically though, can you imagine there being so many CEOs knowing that this thing is going on and being forced to lie about it, and not one of them spilling the beans? Even if the gov tries to arrest them for leaking classified information, they'd be near-impossible to convict following the inevitable massive public outcry.
You don't get to be CEO unless you can learn to lie & keep secrets. OTOH, I'm more skeptical about the implementation side. Have you ever set up a feed between two different organizations that needs to transmit a massive amount of data in real-time? It's an immensely complicated undertaking requiring a whole team on both sides, with managers, engineers, techwriters, QA, and support staff. It seems a little unbelievab…
Implementation side would definitely be very difficult, but you could screen the candidates for those who are sympathetic toward it. Ensure they understand how important it is that the program stays secret. Keep retention high, and perhaps even have some ongoing benefits for any employees who do churn but were part of the program. It definitely wouldn't be easy, but I think it is doable.