It's true in SF, NY and few other places in US where cost of housing is determined by ability to pay. In the rest of the country cost of housing is a cost of building a house/rental property with a reasonable margin on top - with almost no correlation with local ability to pay (as long as it's higher than cost of building or maintaining a housing unit). If you increase property taxes, it will increase rental prices.
I am saying that supply and demand are not working in SF/NY and a few other places. Or to be more exact supply is non-elastic - increase in demand does not increase supply. In cities with available land if there is a demand for housing, you just build more housing.