Totally false if you're a US citizen.
Also false if you are a Mexican citizen.
In the latter case, first of all you need a valid visa. It will probably suffice, if you know what you're going to do in your visit to the US and tell it properly to the immigration officer.
But if you're young and slovenly dressed, have no stay address in the US and the officer is in a bad mood, s/he may ask for some proof of your financial possibilities (a credit card might do, or perhaps some US cash).
As a Mexican citizen I've entered the US a couple dozen times and only once I was asked to show money. I was 19, it was 1973, arrived by bus to the border, late night, explained that I was a student but my school was on a strike...