Not really true, it's just that your socioeconomic caste is the biggest deciding factor by far in your chances to climb up that ladder. Poor white people who then become "successful" economically do exist, and the fact that they exist is used as a massive propoganda point by conservatives, but it's exceedingly rare and it's not something a majority can achieve even if they're the hardest workers on the planet... but to poor non-white immigrants, the poor white guy's chance of succeeding seems extraordinarily high in comparison, because given the same opportunities the nonwhite immigrant just won't have access to most of them. Same goes for a black woman, or a trans person, or someone with an invisible or clearly visible disability.

Sure, "rock bottom" is a permanent state of being for many people that get there, but different peoples' "rock bottom" is worse than others (on average) regardless of that. As a white person who's disabilities are pretty invisible, I can often camoflauge myself as one of the "upper castes" and enjoy many of the same benefits and assumptions as a richer white person might, the same isn't as true for someone who is latino or very outwardly disabled presenting or something. The class divide, despite what a lot of people would try to convince you, is not the only problem, nor is it the root of all other socioeconomic inequality (though it does exacerbate it).