You could say that this is not necessarily true, even though we all wish it was. There's an endless supply of people out there who work really really hard and yet they never become billionaires, in fact they might be living at poverty levels.
It's kind of a cool myth, but social mobility doesn't quite work that way.
I see two separate assertions : one, that hard work lifts you out of poverty. Two, handouts don't result in lasting changes in someone's economic status. I agree with you on the first. As for the second, that seems true enough: few welfare recipients have their lives transformed by the payments.
It's kind of a cool myth, but social mobility doesn't quite work that way.