What about full blooded "white spaniards" in South America who never married outside of "white spanish"
I think these people are rarer than you might think considering the ethnic diversity of South America. However, this exception still wouldn't change the fact that such people are culturally Hispanic and, by and large, descend from a region that is ethically diverse. If someone is born in Africa, for example, then they are still considered African, even if they are descended from the Dutch. Brazilians, on the other hand, despite descended from South America, I wouldn't consider Hispanic but unique in and of themselves.
I think Aregentina/Uruguay might have tons of spanish or italian only descendants although they won't consider themselves spanish/italian.
Genetic studies chronicling Argentinians have the average person with some admixture of Native American (higher than 10% on average), and in rarer cases some smaller percentage of African ancestry as well. So these are exactly are the situations where one would say they are Hispanic rather than European because, in actuality, they are more diverse than Italians or even Spaniards. As food for thought, one might note that interracial admixture is (perhaps surprisingly) present in Europe as well, although in much more isolated doses. Samples taken from white Portugese people on specific islands, for instance, have Sub-Saharan haplotypes, which indicates some native person(s) have African ancestors.