> In an alternate universe the U.S. government created a corporation to run Social Security. It mandated that people participate in it. Everyone called it a pension system because that it what it is

If the U.S. then explicitly guaranteed that corporation's liabilities, sure.

> All pension systems are subject to amendment. Many pension systems have been amended over the years

No. Many state legislatures, for instance, are constitutionally prohibited from fucking with certain obligations, commonly pensions.