As someone who knows many landlords: Completely wrong.
They buy properties with a loan. They pay interest on that loan. The money the renter pays goes towards the interest payments. Renters are essentially buying the properties for the owners.
And landlords can keep deducting it, no matter how many properties. Homeowners can deduct only for two houses. And renters deduct none of it. The landlords literally deduct what their tenants are paying (interest, which is part of their rent).
And not sure about your other comment, but rarely do renters of similar size houses/apartments pay less than homeowners. As an example, my house I bought only a few years ago: I pay just a little more than some 3 bedroom apartments (which are much smaller than my house). Most 3 bedroom apartments in desirable areas in my city pay more in rent than my monthly payment.
And then with all the deductions I was getting, I was effectively paying less than most 2 bedroom apartments, and some single bedroom apartments. And if I take into account the amount going towards the principle, I'm paying about the same as most single bedroom apartments in my area.
I did not put in a huge down payment. Less than 20%, in fact.