There’s significantly more to being educated than knowing facts, and that (IME) is where the self-educated tend not to be as strong as those who have been through some kind of assessment process.
Anyway, I recently stumbled across an article that I think is relevant to this thread:
But for obvious reasons almost no attention has been paid to the appalling decline of literacy among college graduates. In December 2005 the U.S. Department of Education released its second National Assessment of Adult Literacy report. The first survey had been taken in 1992 using a sample that accurately represented the entire adult population age 25 and up. The NAAL grouped respondents into four categories, below basic, basic, intermediate, and proficient according to their reading abilities. These were tested in three categories of literacy labeled prose, document, and quantitative. Prose literacy denotes the ability to search, comprehend, and use information in continuous texts. Document literacy means the ability to do these same things employing noncontinuous texts in various formats. Quantitative literacy involves having the knowledge and skills to work with numbers and figures, a figure that changed very little between 1992 and 2003 when the second assessment was made.
The other two categories showed a precipitous decline in literacy among college graduates aged 25 and older. In 1992 40 percent of all graduates were found to be proficient in prose and 37 percent demonstrated proficiency in document literacy. In 2003 the percentages were 31 percent and 25 percent respectively. Over a period of eleven years the proficiency of all approximately 37 million college graduates had declined sharply, in prose by nearly a quarter and in document literacy by almost a third. (The performance of high school graduates declined as well, from 5 to 4 percent in prose and 6 to 5 percent in document proficiency.) Apart from the oldest graduates having died the addition of ten, or at most eleven, graduating classes to the pool of college graduates, meant that the members of these classes had to have scored very badly indeed to drag down the averages of the entire population by so much.