There’s also the simple logic that people who are vaccinated against COVID are probably more likely to be vaccinated in general. They are more likely to have flu and pneumonia shots, and to get the adult DPT boosters. If they happened not to have gotten childhood shots, or gotten them irregularly, they are more likely to have made up for gaps in their records.
The last might be a factor of education, where education → affluence → access to healthcare, but the shots that are standard adult shots are not really. You can get them free or very cheap lots of places, Medicare pays for them, and many employers provide them-- some even encourage them in the strongest way possible, so that you have to be actively anti-vax, not just lazy or uninformed, not to get them.
Also, IIRC, when reading about anti-vax ideas and autism, being actively anti-vax is often something you find in educated people– as opposed to the “vaccine hesitant,” or those questioning vaccine mandates under “rights,” as opposed to the value of vaccines themselves. Generally though, educated anti-vaxxers are not people who are Nobel Laureates in medicine-- they will often be people with PhDs in folklore who are so convinced of their superior intellects, that they won’t listen to anything anyone else has to say-- especially someone with a mere bachelor’s degree, even if it’s in biochemistry.
However, surveys of people’s level of education often just look at the level of advancement, and not the relevance to whatever topic is being examined. That’s how you get something like “20% of college-educated people believe in creationism.” Sure. Because half of them went to “bible colleges,” and the other half majored in Theater, Physical Education, or Guitar Performance (all fine disciplines in themselves, but don’t require one to study the origin of life or the age and shape of the earth to graduate).
But your people with PhDs in folklore and Guitar performance, who decided not to get the COVID vaccine, while under some spell of Durning-Kruger, probably still get their colonoscopies and mammograms, and insist the vaccine is “a special case” [it isn’t]. They also have great insurance, so their kids don’t develop terrible chronic conditions from under-treated infections.