"Utter Bollocks. It very much helps to come from a privileged or at least well off background to get you where you want to be. Having the confidence even if you don't have the cash can come from the background and opportunities you were given as a kid."
It can help, but it's not the be all and end all; I was brought up alone by an alcoholic, in the sort of conditions that would feature in a modern Childline ad (I brought myself up from around age 12, including handling the bills, etc); and yet, I'm doing pretty well for myself despite being disadvantaged in almost every important respect from a first-world standpoint, not to mention living in the arse end of nowhere, to boot.
Opportunities come easier if you have the benefit of a 'lucky' upbringing, but I've mostly got to where I am today (which isn't much, but it's fine) by wit, intellect and a burning urge to prove everyone who said I'd amount to nothing because I was the local poor kid utterly, blindingly wrong.
Opportunity smooths the path, but incentive and attitude are far, far more important IMHO, and make you take the path. Incentive makes you smash down the barriers and get places.