Which they obtain at lower cost than a poor person could.The reality is that the rich do have a higher standard of living.
Every standard of living costs the rich less than the poor. Including the minimum one, which they can choose whenever they want to.
So their minimum cost of living is lower.
btw: You have never met a miser? Odd. They are not that rare. My favorite was a neighbor of mine, old guy, who had worked as a janitor his entire life and made himself a small fortune. He was retired. His routine included coffee and doughnuts - free - in the VIP lounge at one of the big downtown banks (where he was not the only guy dressed from dumpsters and dead acquaintances, although he may have been the only one who used twist ties from bread bags to fasten his shoes) followed by a stroll to the Dorothy Day Center for midday charity chile, and a stroll home with a newspaper or magazine fished from a bin. He was the first self-made millionaire I ever shook hands with. He had the lowest cost of living I have ever seen implemented - but even he could have lowered it a notch by using his wealth: he insisted on living in a big city in northern America, and renting a room of his own. He could have made other arrangements, because he could have fronted the cash for them - his choice.