Earlier quoted context omitted.
Important qualifier on that that's missed for most "the very rich". The "rich" are often quite penny pinchers. My grandfather is "rich" (several millions, and in a very cheap place to live in the midwest) but he lived his entire life being extremely strict on spending and controlled personal finances very carefully. He still complains when there's large money to be spent on something that should be cheap.
From what I understand, that penny pinching is often why the rich are rich (excluding those born into more wealth than they can spend). Edit: I'm getting the impression that a large subset of people replying ignored my parenthetical comment.
As to why this myth persists, I guess it goes well with American puritanical roots. Many possibly don't belief in a strict correlation, if not causality, of everyone's financial situation and their individual moral character, but still promote the idea. See also: prosperity gospel, Ayn Rand.