The article avoids a bigger concern which is the size of government spending. In 1960 (I couldn't find older data) federal government spending was $144B. If we adjust for inflation, today's spending would be $1.6T. It's $9.7T.
Perhaps the rich are paying less, but a government that increases spending by 6x is certainly contributing to the problem.
Population has doubled size 1950 explaining some of the spending increases and spreading out some of the costs, but not all. It would be interesting to see if the number of "millionaires" has rise proportionally.