European aristocracy doesn’t have a lot of taboos left around marrying from the lower classes.
Maybe the most prominent example is Victoria, the Crown Princess of Sweden. She married her personal trainer, a gym entrepreneur and son of an ordinary civil servant, who received the titles of Prince and Duke.
Europeans have been famous for marrying "rich but common" Americans for so long it's a running joke in Wodehouse books.
Hell, Harry did it too.
I agree and you've summarised what I wanted to say.
One addition: social mobility is possible in almost any class based society. So using one such example does not prove that class in USA==wealth.
For context, Schwarzenegger met Maria Shriver after he had gotten the Golden Globe Award for New Star of the Year – Actor for Stay Hungry(1976) while in an open relationship with another woman and married around a decade later after his big breakout in Conan and Terminator.
He was by then already a successful bodybuilder, she didn't really marry a bricklayer, and anyway it's not like you can't find similar example in European nobility.