The distinction, as I understood it, was between public UBI and Social Security (and other earned benefits) - not between differing sorts of retirement plans of which Social Security is one (and one which every worker is required to participate in).
If one never worked and were not eligible on someone else's earning record (such as by being the spouse of someone who worked), one will receive zero Social Security old age benefits. This is very, very different than UBI which completely ignores both an individual's contributions to the system (as well as the individual's need for the system's benefits).
It is true that one can't rely on the government to fulfill their implied obligation to pay full Social Security benefits in retirement because the government has no such obligation. In theory Congress could cancel all future Social Security benefits from next month on, retain the payroll taxes, and spend the rest of the ever dwindling OASDI trust fund and the revenue from the ongoing payroll taxes on something else - such as an expanded defense budget. However, the odds of something this extreme happening is very remote (as it would likely result in no member of Congress who voted for this being reelected and them being replaced by candidates who pledged to restore benefit payments). It is, however, entirely possible that SS retirement benefits will be cut across the board when the OASDI trust fund runs dry (that date varies from year to year based on the economy and resulting projections, but the 2024 trustee's report projects that will happen in 2033 - sooner than the 2034 date projected in their 2022 report).
The Social Security OASDI Trust Fund was supposed to be weakly similar to the "capitalization model" you describe - that's why it was allowed to grow, at its maximum point, to $2.91T in 2020 rather than the program being strictly "Pay As You Go". However the failure of Congress to act decisively and consistently in the past to keep this model solvent (Social Security being described as "The Third Rail" in politics) will likely result in benefit cuts in the future (the form of those cuts remains the "trillion dollar question").
However a private annuity company, public pension fund, or private pension fund can also become insolvent and, if enough did, the government and quasi-government agencies, such as the Pension Benefit Guaranty Corporation and the various state guaranty associations, may be unable to backstop the programs.