If all the people are currently getting a deal on rents, then all the rents are too low, and the landlords will start raising rents until they stabilize on what people are willing to pay. Nowhere does the landlords' cost come into this equation.
This whole "taxes get passed onto the consumers" fallacy is just another bit of anti-tax/anti-gubmint propaganda.
You're right, but in the end you're wrong. The missing step here is people who own properties have other places they can put their money. If, as a result of increased taxes, owning rentals isn't bringing in enough profit to justify the extra hassle, there will be people getting out of the business.
This trickles down to developers not getting the prices they need to get and not building new developments. With constrained supply rents will go up.
The other option is landlords will do the same sort of "decontenting" car companies do in a tight market. They'll cut maintenance staff, paint less, spend less on renovations. Over time your rent will be the same, but the value of what you receive will go down.
The idea that "taxes get passed on to consumers" is not a fallacy - you can see it at work every time taxes go up. Business owners are like anybody else - when their wages get cut they take a look at their options.
Landlords don't eat tax increases. Anywhere, ever.