I would find that statement hard to believe. Individual and corporate income taxes account for less than 60% of the Federal government’s revenue, so it seems unlikely on its face that this statement could be true.
If I remember the numbers from one of the studies in a link on this thread, we are only dealing with less than 15 percent of the total Fed income being returned to the States. The number was around 600 billion actually returned. So I could very easily see it as a true number. The real answer might be hiding in the total amount individual taxpayers contribute to the Fed.
As you and others have stated, it is a very complicated subject, that perhaps should be greatly simplified.
It's true that the Federal government actually pays very little money to State governments. But the Federal government pays enormous piles of money to individuals in the form of wages, benefits, Social Security payments, Medicare, etc. When you see a comparison of Federal taxes paid vs. Federal expenditures in any given State (like the list I show in Post #97), the "Federal expenditures" for a State include all of the payments made to individuals who live in that State.