That sounds an awful lot like "If you've got nothing to hide, you should tell us what you're doing".
I'm all for transparent governments, but I don't think transparency should be a requirement of a private company.
So a transparent government is well and good for those who need utmost secrecy. They just contract out to the non-transparent companies!
I am not saying it's like "If you've got nothing to hide, you should tell us what you're doing". I am saying that you have to be able to manage the public image of your company even if it is a private company. Or things like that will happen and it will be hard to restore your reputation over people you ignored.
It's all about the communication, public image, reputation... There are even companies dedicated to do that for you. I don't know for instance they should use the same idea behind their website: a company of high quality dedicated to BigData, and advertise that in every public media with nothing related to war, secrecy or others things... Just a company providing high value products to who you want.
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!
Also, I don't think it's entirely fair to construct a black-and-white dichotomy between government and private company. Companies working on government contracts are by definition somewhere between the two, so perhaps it's fair to demand transparency somewhere in between? I don't know where to draw those lines, I'm just trying to point out that there isn't, logically, much room for absolute arguments about private vs public on this particular topic.