The idea here is basically correct. However, this statement is usually joined to a second statement to the effect that this principle was violated by subsequent Administrations. However, there has never been any change in the way the Social Security program is financed or the way that Social Security payroll taxes are used by the federal government.
The Social Security Trust Fund was created in 1939 as part of the Amendments enacted in that year. From its inception, the Trust Fund has always worked the same way. The Social Security Trust Fund has never been "put into the general fund of the government."
Most likely this myth comes from a confusion between the financing of the Social Security program and the way the Social Security Trust Fund is treated in federal budget accounting. Starting in 1969 (due to action by the Johnson Administration in 1968) the transactions to the Trust Fund were included in what is known as the "unified budget." This means that every function of the federal government is included in a single budget. This is sometimes described by saying that the Social Security Trust Funds are "on-budget." This budget treatment of the Social Security Trust Fund continued until 1990 when the Trust Funds were again taken "off-budget." This means only that they are shown as a separate account in the federal budget. But whether the Trust Funds are "on-budget" or "off-budget" is primarily a question of accounting practices--it has no affect on the actual operations of the Trust Fund itself.
Thanks for posting your great research.