Graduate students are only superficially poor. They can be better called "temporarily out of money". They are not at the life's dead end, on the contrary, they invest heavily in their future lives. Very different from the poor people lacking education to get ahead as well as means to get the education. Different from those poor people who lack the capability (or habit?) of planning their life. In addition, grad students typically do not have families and kids to take care of.
I never argued any of the points you refute. I merely pointed out that when you are poor (temporarily or not) and lack a car, you do end up paying more for stuff that you have to buy nearby.