I don’t think that’s true. The landlord can cancel this “option” reasonably easily so it is quite different from selling a call.

I look at it like: the fair value for rent is x. The current rent is y > x. If the landlord nominally lowers the rent, they cannot raise it to as high a value next year, and they do not want to do this. Therefore they are incentivised to (effectively) give the tenant money along with the rent to decrease y without changing the nominal rent and giving up on the right to increase it.