The supplier is necessary in both tenant and property table as the supplier could be different for each.
With regards to your other question, this is a bit more difficult to explain. The Landlord is the owner of the property. He then will give his property to a company (supplier) who will in turn give the Landlord a regular rental payment regardless whether there are tenants in the property or not. The company (supplier) then supplies the council with the property for tenants to move into. We need this recorded as the rental income is different dependent on what supplier the property is with. The supplier is selected under the tenant and not the property, as the property can move between suppliers and changes dependent on the tenant... I hope that makes some sense to you.