There's really two (equally valid) ways to look at this, from an accounting point of view.
1) SSA is independent. It has liabilities (the promises made to enrollees), and assets (the trust fund). Liabilities exceed assets in the long run, but until then (currently projected as 2034) the system is fine. The federal government, on the other hand, needs to count those liabilities at full value. This means government debt is significantly higher than generally reported, the Clinton surpluses never actually happened, and a lot of spending decision, in retrospect, look quite reckless.
2) SSA is not independent, but is part of the federal government. Social security has liabilities (the promises made to enrollees), but the trust fund is a wash. This means that the lower "net" totals for government debt are technically correct, and that there was a budget surplus in the 90s...but it also means that no provision was made to cover those liabilities; the system is being run strictly on a pay-as-you-go basis. And while they may not be technically debt, given the scale of the liabilities social security represents to the federal government, a lot of spending decisions, in retrospect, look quite reckless.
What's important to note is that these two stories are completely identical. It's like arguing whether a liter of water weighs 1kg or 2.2lbs; the answer is "both". :) In both cases the money collected via the payroll tax was used to fund general expenditures, leaving an unfunded liability. The size of the liability isn't in question, nor is the matter of who has to pay it. It's really just a qyestion of what you label the boxes.
> it doesn't make a whole lot of sense to think of the government as saving money specifically for the future expenses of retirees.
That's not inherent in the concept of a pension system. It could have been run on a funded basis, with actual savings accounts; it was not due to political reasons. I took toomuchtodo to be decrying that fact. Yes, the system we have is a pay-as-you-go system, but in retrospect doesn't that seem like a pretty poor idea?
Also:
> the Fed can retire government debt if it wants to, just by creating new money out of thin air and buying treasuries
That is legally impossible. (It also wouldn't work from an economic POV; it's effectively the same thing as just printing money to pay for SSA liabilities directly, and we know that funding government directly via the printing presses doesn't work.)