Or perhaps they comprehend it just fine, but they make a choice you disagree with
No, and that's the entire point of the article linked at the top of this page. They are not making a choice. A thought pops into their head and they go with it, rather than thinking about other options. Or if they do consider other options they don't make the choice that would be most helpful to them.
The 3 sodas a day example was not meant to be a tuition fund on its own - it is illustrating the lack of connection people make. The hypothetical person involved is not going to pay full tuition out of pocket, so you can add grants into your math as well.
It provides no guidance on a viable strategy for emerging from that environment, and your flippant advice about simply not drinking soda is symptomatic of another, perhaps larger problem, that poor people face: Prejudice
There is absolutely no basis for your conclusion. People can't think their way out of poverty because of the baggage that comes along with poverty. I don't see how the failure to connect immediate spending with future spending falls outside of that inability.
The people I have known who earned $10/hr or less buy stupid things and complain about having no money. They don't understand the difference between principal and interest, and don't seek lower interest rates on things like car loans. They are not stupid people, they just can't think about money. Getting out of poverty is not simple math. But we aren't talking about getting out of poverty. This is simple money management.
When I say "stupid things" up there, am I judging their purchases according to my own prejudices? Of course. Because I have good money management skills and they don't. Like buying an expensive car that has to be returned because they can't afford the payments. They lost money that could have gone towards owning a car, and have to start over. Stupid.
The far-reaching conclusions in the article seem to be the author's opinion and have nothing to do with the research at hand.
The finding further undercuts the theory that poor people, through inherent weakness, are responsible for their own poverty â" or that they ought to be able to lift themselves out of it with enough effort
That is opinion, outside the scope of the study. The disconnect between immediate and future spending is supported by the research presented.
Consider that, and consider than soda is not the only extra people can do without if they really want to be financially better off. Consider the role of grants and scholarships, and do your math again. I'm sure you will realize it's not so flippant of a comment.