Yes! Insightful - the cost of living varies by location. Get this man an Nobel prize for his groundbreaking work.
FYI the literal definition of rich is having a great deal of money or assets. It's a measure of stock (total savings) not flow (annual income). So again a snap shot income is not a great determinant of being rich. $250k is unquestionably comfortable and allows you to pay the bills and do all the regular things a person could do.
Furthermore, the cost of living across states by nearly 100% (2x) from the least expensive (Mississippi) to least expensive (Hawaii). However wealth disparity in America is over1000x worse than income disparity!* So sure depending on where you live you may be middle class or upper middle class but moving can't make you rich. It could at best double the value of your savings.
* The annual income of the top 1% is 3% higher than income of the bottom 40%, however, the wealth of the top 1% is 13,936% higher than wealth of the bottom 40%.