I disagree with your sentiment. Being public/private doesn't make one more/less trustworthy. I would posit it is the business model of the company itself that should be given scrutiny.
Is this the normal understanding of private/public companies? I don't own the USPS nor do I own the national parks. However, taxes pay for them, so we are given access to them. NASA is another example. I can't just walk into the JPL and start using a computer. However, any data that is produced by NASA, I can use just like I can use the national parks.
Ostensibly, no. But practically, there is a single majority shareholder who can choose to do pretty much whatever he wants with the company. So... kind of?