I admit it's not a perfect analogy, but it's the best I could come up with. Intellectual property is a difficult concept, since it's intangible--it's difficult to think of owning an idea in the same way as one would own a car or a house.
The difference between your analogy and mine is that, in yours, you never had title to the car--in other words, you never owned anything, regardless of what you believed. It's sort of like the old saw about buying the Brooklyn Bridge--I can convey to you all of my rights in the Brooklyn Bridge (all none of them) for a certain sum of money. By contrast, in my hypothetical, the CRAP is the absolute arbiter of who owns what real property--if they say you own something, you own it...even if it turns out they were wrong. They actually can convey meaningful legal rights to you, unlike the car thief. Maybe they take it away later, but for as long as you have legal rights, they are enforceable.
(Yes, I do this for a living.)