Black is 10.0% of all vaccinated while making up 12.4% of population.
White (non-hispanic) is 61.5% of all vaccinated while making up 61.2% of the population.
So we're talking ~2.4 points behind at worst (stats are from the CDC link in your article). For comparison we're talking about more than a 10 point gap when comparing counties by political affilation. https://www.kff.org/policy-watch/the-red-blue-divide-in-covi...