First of all, the statement was that anyone can become rich, which is false.
Also, the moved goal post is a straw man, of course. We're not talking about "rich" - we're talking about decades of stagnant income for the vast majority, soaring income and wealth for a few at the top that has resulted in a shrinking middle class, which I'd define as able to work a normal job, and afford healthcare, education including college for your children, vacations and a secure retirement.
And society's "responsibility" is in my view to set the rules of the game (the "market") so that we have broad prosperity, and the entire income scale shares in the gains of productivity, rising GDP, national wealth. Unfortunately there isn't (to my knowledge) any example anywhere in history of a 'natural' large middle class. A couple of others are discussing this in this thread - but if you find a large and prosperous "middle class" what you also find are strong government, progressive taxes, and a fairly significant amount of income "redistribution" either directly such as through national healthcare and income guarantees of sorts (welfare, EITC, food stamps, rent subsidies in the U.S., etc.) and likely some form of wage supports such as through unions or minimum wages and the like.
I think that's entirely appropriate. Government doesn't exist to maximize GDP or the S&P 500. It serves the U.S. - 350 million or so individuals, and the economic policy should focus on the broad population.
If you have any examples otherwise, I'd love to learn something new this week!