Yes! Exactly! That's why I said "you're almost there". You almost had the right idea, but you needed the exact distinction between owning possessions and property. This distinction, plus a little bit of critical reflection, should be enough to come to the conclusion that landlordism is exploitative. The FAQ explicitly sketches out the argument that landlords exploit people.

The land monopoly consists of enforcement by government of land titles which do not rest upon personal occupancy and use. It also includes making the squatting of abandoned housing and other forms of property illegal. This leads to ground-rent, by which landlords get payment for letting others use the land they own but do not actually cultivate or use. It also allows the ownership and control of natural resources like oil, gas, coal and timber. This monopoly is particularly exploitative as the owner cannot claim to have created the land or its resources. It was available to all until the landlord claimed it by fencing it off and barring others from using it.