This is true if you're looking at rent prices in a cost model, where the price of rent is basically the cost of providing housing plus a little extra for profit

This is true if you're looking at rent prices in a cost model, where the price of rent is basically the cost of providing housing plus a little extra for profit, similar to low-margin commodities like basic groceries. But in a high demand area with constrained supply, it's more of a supply & demand model: landlords charge what the market will bear, which is mostly based on how many people there are around with decent/high-paying jobs. Prices haven't risen rapidly in recent years because the actual cost of building housing rapidly increased, obviously. So using the latter model, increased property taxes probably wouldn't have much impact on rent prices.