The article would be more useful if, along with the table of black vaccination rates vs educational level, it had the tables for other racial groups.
Later data from US Census Bureau surveys.[2] While the Census Bureau did not summarize vaccine hesitation, race, and educational level, they offer downloads of the entire data set of poll replies. (192MB, CSV format), so you can do that yourself. Next data set available August 11th. Good project for big data people.
[1] https://news.usc.edu/182848/education-covid-19-vaccine-safet...
[2] https://public.tableau.com/views/HouseholdPulseSurveyCovid-1...
He's starting with an assumption that disregards any factors that could make the hypothesis he's trying to disprove correct, and so of course the statistics come out in his favor.
It's a very short post. About a two minute read. No guesswork needed about assumptions he's making, you can just read the post for yourself.
It would also be helpful if he didn't limit it to people aged 30-50. What do the rates look like outside of this band?