You are correct. Many wealthy people get to be that way precisely because they are penny-pinchers.
Just a quick story about that. There’s a legendary furniture store in Omaha called Nebraska Furniture Mart. After her husband died, Rose Blumkin who is known to everyone as Mrs. B, discovered that she could get a 1 or 2% discount by paying within 10 days. Being born poor in Belarus, she new free money when she saw it! Even though furniture stores are notoriously slow to pay, for a number of years the only money she took as a salary came from those discounts. In the end she sold to Warren Buffet who considered it one of the best deals he ever made.
Just an example of how frugality pays off and MBAs aren’t always the smartest people on the planet.