When I speak to people in the city (which in fact does happen, since I do live here, reporting aside), they often see the fact that new development occurs in the same places at times when housing costs are spiking. Consequently, they often reach the conclusion that new development is causing price increases and that the best way to moderate price increases is to moderate the pace of new development. These charts indicate, I think, that this is a mistake. That both new construction and higher prices are caused by higher demand for housing, and that DC is experiencing an above-average rate of housing cost increases because we’re experiencing a below-average rate of issuing permits for new construction.
I think it is the case that more people moving into neighborhoods, especially relatively blighted ones, can lead to further price increases. The mechanism is fairly simple. More people equals more demand for local goods and services, which means greater variety of availability of local goods and services, which makes a neighborhood even more attractive, further boosting demand for housing units in that neighborhood.
As for the initial trigger of more people moving in, that could be increases in housing prices elsewhere, a change in consumer preference for type of housing, a reduction in the local crime rate, etc. The point is that more people can lead to a better neighborhood which can lead to more demand and higher prices. It isn't necessarily incorrect to perceive new development as the cause of higher prices.