Semi-true. That's the theory behind it, but in most of it's history, SS has provided a surplus (it's had a deficit in only 13 years, mostly in the late 70s and early 80s) which is accounted for separately than the general fund. Until the 90's under Clinton this was kept completely separate and not touched except to handle deficits of SS itself, but Clinton signed legislation allowing the government to borrow from the SS Trust to pay into the general fund (one of the reasons he could balance the budget) turning the trust into Treasury Bonds earning 3% interest at the same time.
The problem right now is the Baby Boom generation about to retire. The sudden jump in retirees is going to stress that kind of system which is why many people want to fundamentally change the system.