For example, recent data from the UK https://assets.publishing.service.gov.uk/government/uploads/... shows [Table 2] that the probability of a case given {vaccinated, unvaccinated} is within a factor of 5 of each other (in fact, for some age groups, the probability of being a "case" is higher for the vaccinated). Also, the probability of being hospitalized is within a factor of 10 between the two groups for all ages [Table 3]. There is no way to get the three orders of magnitude difference that you quote given these figures.
> why are Americans overwhelmingly flat out wrong on this statistic?
Speaking for myself, if somebody called my phone out of the blue to ask me a stupid question (are you republican or democrat? what's the probability of hospitalization?) I would make up an answer just to troll them. I would probably mention Bill Gates' chips as well. What's my incentive to tell the truth, given that I believe that all polls and media are a bunch of liars?