The article simply shows this is not born out by evidence in certain cities. That doesn't mean it can't be true in others.

In general, it seems pretty clear that if a city is attracting new people, the article is right: whatever else you do, keeping the housing supply limited will increase prices. The mistake NIMBYs make is typically to assume the city population won't grow if they prevent new housing stock, but this is not the case - even if a city has tight regulations on no new housing, adjacent communities will likely not, and will simply cause sprawl from there.

However, there may be cities that are not seeing significant population growth, and are still seeing significant price increases, for various other reasons (tourism, realty as investment, gentrification, etc).