"If you have an enforceable claim on something, then you own it. If your claim is not enforceable then you possess it."
Let me repeat myself for clarity. You can own a property with a reversion. You can own a leashold with a reversion. They are both enforceable claims. You can exclude people for the term of your lease. How is that not an enforceable claim? You said an enforceable claim means ownership. I think you were mistaken in saying because it's not true.
Now you are caveating it to portions of a whole. But a leasehold is for the entirety, just for a term.