Actually, people don't become wealthy from saving their money. They become wealthy through investments; and that's even when such investments become profitable. This is the simple reason billionaires always look for ways to reinvest whatever that's left of their earnings after setting aside what's for their daily running cost. The fact remains that only those without investment plans let their money lie idle without putting it to use. Savers who don't have any investments is meaningless.
But you are talking about rich people who already have a lot of wealth and profitable investments. And what to do when you still have nothing, how to build this fortune, that will generate a constant financial flow?