Yes, nobody is disputing that fact.
That makes no sense. Of course plenty of self-identified white people, for example, have significant amounts of non-white ancestry, even when they have stereotypically “white” physical traits. Where exactly are you drawing the line between “little to no” and “significant” ancestry? Can you give us a number on this, please, or at least a numerical range?
Not a logically valid syllogism, though. You’re attempting to argue essentially as follows:
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Individual intelligence appears according to all the available evidence to have a strong genetic component.
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Groups of racially white and (East/South) Asian people generally share “most” (although you shy away from defining “most”) of their genetic ancestry with other white and Asian people, respectively.
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Groups of racially white and Asian people tend to score higher on IQ tests than other racial groups.
Attempted conclusion. Therefore, the group IQ score differences are probably significantly due to genetic factors associated with these racial groups.
There are logical holes in that argument that you can drive a truck through, to wit:
Correlation isn’t causation. It’s not as though there are no group differences between whites/Asians and other groups except their genetic ones. Unless you can control for all the non-genetic causes of average differences between racial groups, your decision to attribute a particular difference to genetic rather than non-genetic causes is just blatant cherrypicking.
Dodging quantification. Many people who self-identify as black actually have more European ancestry than many people who self-identify as white. Especially in the US, there is a huge variation in the percentage of European ancestry found among people racially classified as black. If IQ scores were strongly dependent on race-linked genes, we would expect to find scores of black-identified testees reflecting their percentage of European ancestry. But AFAIK no such phenomenon has ever been found. (In fact, AFAICT it’s the other way around: children of recent African immigrants with much less European ancestry than most African Americans tend to do better on IQ tests.)
You are sweeping all of these inconvenient facts under the rug by clinging to very crudely delineated qualitative racial-group classifications and demanding that they be considered genetically meaningful without looking closely at the actual amounts of various genetic heritage.
Confusing heritability with genetic determination. As I pointed out to octopus with the above-linked cite, even the undeniable heritability of intelligence can involve a lot of non-genetically determined factors. You are mixing up different concepts and phenomena in an ill-informed sludge and then pouting that other people are “refusing to see” your obvious self-evident truth.