The American Dream is indeed a powerful concept, however, it is crucially important to note that this power comes from what it promises, not what it provides. This saying came to be because the job market in America is objectively better than the wars, drug cartels, murders, kidnappings, arranged marriages, etc... in certain third world countries. America could have had half of the jobs we can offer and still have framed it that way because it was the objective lesser of all evils. Yet, when a person of color immigrates to America to achieve this dream they are given the absolute bare minimum because we know it is still better than what they came from.
Is it a dream compared to where they came from? Sure. A dream in the climate of America, considering what its citizens are given (i.e. minimum wage, voting rights, citizen rights, better opportunities, etc...)? Not by a long shot. It is very unfortunate, but true, and it must be recognized.