I agree with the sentiment but for all intents and purposes, pretty much any organ within a State is run like a for-profit corporation. Their "income" is taxation, fines, etc.
I believe the stark difference is, that a private company can spend what it earns, while the budget of government agencies or the military is basically arbitrary (committee-decided). Usually we would weigh agency spending against the value their service directly or indirectly provides. While a company's spending is weighed against its direct earnings.
Well, a private company can raise capital, so it can spend beyond what it earns, similarly to how the government budget can exceed tax receipts by issuance of debt and other methods.
The military budget is decided by a sort of committee (many of them, in fact, and not just Congress), but private companies all have ways of parceling out a budget as well, it's not as if most staff are literally paid out of their own personal direct sales. And the way that budget is decided almost invariably involves committees. The current DoD funding model was actually taken from what Ford Motor Co. used in the 60s.
When we were at risk of government shutdown earlier in the week, our office within the agency was relatively immune to the potential shutdown as our civilian staff are nearly all paid out of 'working capital' funds which are modeled after a direct earnings model, rather than being paid out of 'appropriated' funds which would have been at risk absent action from Congress.