There's a simple way to visualize why is not true:
You're renting a property for $1000/mo. Whatever the owner is paying for property taxes, you don't know.
Then, property taxes go up by $200/mo. Do you think your rent won't go up by at least $200/mo as a direct consequence of the tax increase? Because it will. Because the renter is of course paying for all costs, including those taxes.
So, before property taxes went up, the landlord could have raised rents by $200/month, but hadn't because..?
Because you don't pre-date inflation.
It is the same as asking why the supermarket doesn't raise the price of milk to what inflation estimates say it'll probably be next year.
Look at it a different way. If the $200/month was a new tax that all renters had to pay, what would happen?
Some landlords are bad at guessing the correct numbers. Others are savants. In aggregate, renters end up paying almost all of it over time if not immediately, and those that don't end up suffering in other ways (when the landlord just stops paying the tax entirely, but taking your rent, the building gets sold, and you don't get to renew the lease because they're going to knock it down and build luxury condos).
What if moving costs $1000, which is another $83 per month over a year.