This is false. The "scheme" can work forever because, unlike a Ponzi scheme, it does NOT promise a fantastically high rate of return on however much money you can be suckered into investing. You get X $$/month, no more no less, from retirement to death.
I DO believe that the temptation to "invest" the vast surpluses of the past was a net bad thing, and I suggest a means of avoiding it above.
What is unsustainable is to hold the retirement age constant while people live longer and longer.