Could you name some of these private companies? I can’t think of any private (i.e. neither public or government owned) company comparable to Apple, Walmart, or large oil companies.
Big, fully private companies are quite fascinating. (I think we're settling on a definition that involves a tight inner circle of ownership, with no stock-market listing and no government control). But they are pretty lightly represented in revenue/size-based lists like the Fortune 500.