I would also consider that the only reason this doesn't hold true for PhDs is that many PhD holders work for universities where the nearly universal access to student loans has upwardly distorted the salaries of college professors.
You said significantly, the difference is marginal between educated workers even in this data set, and as I stated this data is biased by inclusion of the admitted higher fed pay before 2010 when federal wage and hiring freezes began. There is no data more current, but anecdotally contractor pay is now higher in the RDT&E domain.
Actually the majority of private sector PhDs are doing post-docs or other poorly compensated work, which should make the private sector lower than fed; the problem is the metric-— they are not using median salary, they are using mean which is distorted by the very high earners in the private sector.