supply, demand and housing costs

I've read numerous blog posts and articles asserting that gentrification or rich foreign investors increase housing costs by increasing demand.  But people who raise this argument aren't always sensitive to the role of supply in the law of supply and demand: for example, one  New York Times article states that increasing demand has raised rents, yet cites one housing advocate's statement that “Increasing the supply is not going to increase the number of affordable units; that is a complete and utter fallacy."  So in other words, increasing demand increases prices, yet increasing supply doesn't lower them.

Of course, this doesn't make sense- if demand matters, so does supply.