Maybe I'm overly logical and can't shake the whole "Necessary and sufficient" aspects of causality [1]. The charitable argument is that working hard can contribute to success but it is neither necessary nor sufficient.
1. https://en.wikipedia.org/wiki/Causality#Necessary_and_suffic...
AFAIK, statistics show that in industrialized Western countries the wealthy people who are seemingly successful (because of their wealth) have inherited most of their wealth or at least benefited extremely from improved conditions provided by already rich parents. In contrast to this, vertical social mobility remains fairly low and the overall gap between poor & middle class and the richest has been increasing in almost all capitalist Western countries since WW2.
So it's not literally a lie, it's just sometimes kind of dishonest and misleading. In most professions it's practically impossible to get rich from hard work.
"With hard work you can be successful in the sense of being able to afford a basic living or being moderately middle class"
There is plenty of empirical evidence that this is not really true. One of the pernicious things about the typical American narrative of success is that it often gets used in the contrapositive. This lets people feel good about discounting anyone viewed as "not successful" (whatever definition you want) as having been personally responsible for their own difficulties, so they can be safely ignored.The problem is exactly that, there are people who think that it is an absolute statement so poor people, unhealthy people, people in bad life conditions, etc are so just because they didn't work hard so they do not deserve any help.