You can't have it both ways. If private companies are going to provide important government services, then those companies must accept a certain measure of public scrutiny and transparency, a much greater measure than an ordinary private company would need to accept.

If the companies don't like it, then they shouldn't bid on government contracts. No one is forcing them to do so. And if you don't think the government should occupy such a large segment of the economy, AWESOME! I'm all for that! I say dismantle the whole military-security-industrial complex!