Actually I'll walk back my claim a little bit. I believe that the value of savings is high for everyone at every level of income, only the value is only high at lower amounts of savings. Let me try to explain.

Suppose you draw a graph where the y-axis is is the amount of "value" in saving, and the x-axis is the amount of money saved.



The red line is the poor person, the blue line is the middle class person, and the green line is the upper middle class person. The benefits of saving for the poor person are in mitigating the risks of minor catastrophes like needing to fix their car or have some money stashed in case they don't get enough hours at work. Past a point though, they just need to be investing their money into increasing their human capital.

So when I said that the poor shouldn't save, what I meant was that they shouldn't save a lot as their need for money in the present is just too great.