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I... find that dubious, in particular about doctorates. Could you link to a source? My guess is that Pew did conduct such a study, but it was misrepresented in some sensationalist news article or somesuch.
Google "Pew Research" and get your data straight from the horse's mouth. Going to a journalist for statistics is like going to a homeopath for medicine. Gallup have also run similar studies, with similar results.
Also, to clarify they didn't have a "Doctoral" category but rather "higher studies". They also provide a demographic breakdown that tells the usual story of socioeconomic disadvantage: Whites* do reasonably well, Hispanics and blacks very poorly. So, not so much "Americans are stupid" but rather "education in the US is woefully inconsistent and correlates strongly with socioeconomic status". Both Gallup and Pew websites are worth a visit. It's just a shame they don't do more international comparisons.
Regarding Mendel, I doubt early geneticists would have thrown out their blending theories after discovering a single new study about peas. Mendel discovered a new mechanism. It's overrepresented in public discourse about genetics simply because it's probably the only simple mechanism of heritability there is.
*I really hate the US "colour classification" of "race". My preference would be ethnicity, but that does become difficult to track after a few generations of cultural mixing. Mind you, I don't know where you'd draw the line between black and white either.
Edit: I could be wrong about the scientific judgement of early geneticists, of course. Given the crap psychiatrists believed I should probably expect it, actually. Still, genetics was never going to become a proper science until people recognised heritability was governed by discrete genes and that there was more than one way those genes can be expressed. Mendel's work definitely helped in that regard, as it showed that traits can skip a generation which helped validate the very concept of genetics itself.