It also appears from my experience on this forum that the prevailing opinion here is that this story is not a myth at all, but I understand there is variance here.
The issue with cost of living is an obvious one that is made in comments here, but that still does nothing to address the individuals/families who _still_ struggle in areas that are much cheaper to live. Yes, the insular view of one who has not lived outside SF is troublesome, but it's dishonest to argue as if there is still not real existing poverty in places with a lower cost of living.
While there are many different ways the socioeconomic status of ones family and upbringing can assist in their own success, there are a myriad of ways in which this is also influenced by systemic features to our society, as well as the historical context of that. Think of racially discriminatory housing policies that have helped lead to wealth gaps in the present.
While rags to riches makes a good story, we also don't talk about failures in business as much as we do the successful enterprises. Referring to individual actions in tandem with family assistance, coming to terms with the subject of meritocracy in our society and individual success, I'd propose we're looking at it the wrong way. The part to evaluate is not how much these things have to do with success, but rather how much can they come back from failure? This paints a rather different picture, as those with more financial security are in a much better position to take risks, make poor decisions, while not being pulled into poverty.
Finally, I'd like to point out that there is a growing skepticism of the liberal world order, the mainstream consensus, status quo, whatever you want to call it. More people are realizing now the varying degrees of ways the system is rigged against common working people. With it comes skepticism of the legitimacy of meritocracy in our current social order. This isn't just coming out of a vacuum.