That's true, as long as you qualify it properly.
The federal government collects most revenue from two different types of taxes: payroll taxes and income taxes.
Social Security is funded solely by the payroll tax. During the period that payroll taxes were higher than benefits, the excess was invested in special obligation Treasury bonds (as specified in the original law).
The net effect was the federal government borrowed from Social Security to finance the deficit, instead of borrowing from buyers of US Treasury bonds. This is where some "accounting fiction" comes in, because borrowing from Social Security doesn't add to the official US government debt.
But, like the redemption of US Treasury Bonds, the redemption of these special obligation bonds comes from the general fund. So, it's either paid by income taxes, or by purchases of additional US Treasury bonds.
As you wrote: it's all taxes. But the source of taxes is important, because it determines who pays it. And, once the Trust Fund is empty, the source becomes even more important.
Social Security cannot borrow money. So, if nothing is done between now and about 2034, benefits will be reduced -- by law -- to what can be sustained by incoming payroll taxes. At the moment, that's estimated to be a 20% reduction.
By your analysis, and it is very good, SS will not run out of money. I say that is so because it is fed at an endless trough of government taxes, borrowings, or fiat currency. The system you describe is the 3 card monte played to hide the fact that is a simple tax and spend welfare scheme designed to generate dependency on the generosity of the Democratic Party.