That assertion depends on an efficient market though, and that is provably not true - the existence of corporate profits demonstrates this, because in an efficient market everyone makes 0 profit, and any rent-seeking will cause every single one of your customers to flee to a competitor who doesn't rent-seek. Everyone has to price as aggressively as possible given the costs, or lose customers to someone who does, and that means zero profit above the actual cost of production/service.
In a world where corporations make profits, some competitors choose to eat the taxes and retain customers, while others may increase prices and lose some customers, and some customers may eat the increased price and remain even though they're getting a worse deal than before. This is the concept of "consumer surplus" vs "producer surplus", and taxes are cutting into those surpluses differently depending on the specifics of each market participant.
All of this has been debated endlessly by economists, in terms of just how much of corporate taxes get passed along to consumers and so on. And the answer seems to be "not zero, and not 100% either", and everything beyond that is up for debate. So no, not "everything is ultimately paid by the consumer", that is the 100% answer and that's pretty clearly wrong in a market where producer-surplus exists.
In reality, real-estate and rents are probably one of the least-efficient markets imaginable. The frictional costs to buying and selling property, and finding a new tenant who might be a problem/deadbeat/etc, or spending a bunch of time apartment-shopping, picking up your life and packing your stuff, and moving, are immense, and all parties involved are highly emotionally invested as well. Landlords are trying to make a long-term calculation about whether the property is going to appreciate - even if they are losing money today, if they expect to make capital gains in the long term it could be worth it. And all parties are operating with minimal information. Out of all the markets in the world, real-estate and rental living spaces are probably one of the least efficient possible.