If I remember correctly, this idea comes from renewed study of the marshmallow test. In that test, children are given a marshmallow and told that if they will wait 15 minutes to eat it, they will get a second marshmallow. The idea is that children who wait to eat their marshmallow will be more successful in life (and better able to save money). However, recent studies indicate that waiting to eat the marshmallow is highly correlated to class. The theory is that poor children are more likely to eat their marshmallows immediately because they live in an environment of scarcity, and they have trouble trusting that the second marshmallow will arrive, while children from middle class families have no such issues because their environments promote a different way of seeing the world.
Regardless of marshmallows, it does make sense that poor people would invest less money. Of course, having a lower salary makes investment more difficult. But the other issue is that poor people have to go out of their way to invest and to even find out how to invest. Jobs at McDonald’s or Walmart don’t generally come with the option of a 401(k). Poor people may well have poor parents who know nothing about investments. And poor people can’t, of course, afford to hire a financial planner. In fact, the only obvious place for poor people to invest is a savings account with their bank — the kind of account with really, really low interest. The savings account is, therefore, a place to stash extra cash for emergencies or to save for desired purchases, not a place to make a return on an investment.
It’s sometimes possible for poor people to invest, of course, but even acquiring the knowledge to do so requires enough luck to know that such a thing is possible (and to have enough money to invest), a lot of independent studying up on methods of investing (and the ability to do that studying — the ability to read, English literacy, internet access, time), and the confidence to choose a savings vehicle, apply for it, and pick investments in spite of one’s lack of expertise.