Not OP, but my parents came with little too. It depends on the situations. "Choosing" to come to the US for shits and giggles, you are absolutely correct on meeting substantial requirements.

Refugees/Asylum-Seekers don't follow the same requirements. It's super hard to nail down as there are different types and most (that I've been aware of) are case-by-case situations. You have war, religious, political, stateless, there's many types and yea... I wouldn't discount what your parents told you. There might be more to the story they don't want to share.