Hello, Shawna Hird. I did not find what you are describing to be true. I am also a premium member. I abandoned my Linden home, rented land, purchased a home through the Marketplace, and placed it on the rental land. I thought I would be able to use the free premium land allotment of 512m (117 prims) to reduce the cost of the rental and add to the allowable prims; however, the Linden premium land/prim allotment is only usable for your Linden home on the mainland. If you rent land/space from anyone else, you will have to fully pay what they are asking for the land/space, plus any applicable land tier fee if you own more than 512m of land.
Hope this helps! --Qbank