If that were the case, wouldn’t we see vaccine skepticism in poorly educated, racist non-Western nations?
On top of that, 'poorly educated' in those countries often means never having been to a proper school, never having finished basic schooling, being illiterate, or lacking access to information (be it the internet or social programs). That kind of skepticism is easier to help, because it stems from a place of actual ignorance, rather than believing oneself to be smarter than everyone else.