I didn't understand the argument either. I've lived all over the country and doubt the poor neighborhoods in Chicago (where I'm from) and Detroit (where I once lived) do their respective cities much good from an investment point of view (whatever that means). Another thing to consider is that poor people use social services, and anyone who has been to Oakland will tell you a lot of those services live downtown. As a former resident of downtown Oakland, I'd say this rule wouldn't hold up there either.
Still, we should invest in poor neighborhoods because it's the right thing to do for the environment as well as the residents of said neighborhoods.
I'd argue the government should start the process by cleaning up brownfield and greyfield (obsolete shopping centers) sites and consolidated land for ease of development. The initial costs are certain to be higher but the returns are larger (in many cases).