They get away with saying they aren't part of the elite because they live in mid-sized cities and aren't part of the cultural elite. In fact, however, they have more money than many of the cultural elites in the big cities that they disdain.
You're right.
Only in the US can millionaires claim not to be in the elite.
The lack of self-awareness is painful.
Compared to the elite of Europe, most of the American elite are new money. And there is also massive inequality
within the elite.
The 10 richest American billionaires are worth at least $60 billion each, and three of them (Bezos, Musk, and Gates) are worth over $100 billion. They each have tens of thousands, if not hundreds of thousands of times the amount of money that a "mere" millionaire has.