I do understand where you're coming from ... but also answer this question.
Say you bought a house, and you were told by all the professionals that the driveway on your property was yours. You've been using said driveway all these years - but - suddenly you find out that the cement company wasn't paid for that driveway by the previous owner. Legally, perhaps, the statute of limitations for liens has passed - but - as you said - deep down - you really know that the cement company wasn't paid - so, what do you do? Do you pay him?
Similarly, say that the company that put in the pool heater wasn't paid. Or the one that put in the pool motors. Nowhere in the title did it say that the pool motors weren't yours. The company that put in the pool motors had plenty of time to pick up their motors. But they didn't. And you always thought they were "your" pool motors. Now, you find out, years later, that the pool motors weren't fully paid for. What do you do? You, of course, would give back those motors and the pool heater. Right?
Lastly, say that the $1,000 built-in beer fridge at the BBQ was used by you for all these years. Again, there is no label on that fridge; you think it's yours by virtue of you buying the house. Let's even say you've had a beer company DELIVER beer almost monthly to "your" beer fridge. Then, again many years later, your neighbor (who has been there all along and KNOWS where you live) suddenly tells you that it's HIS beer fridge that is in your BBQ after all. He even produces a bill of sale that says he bought that beer fridge many years ago. What do you do?
Do you give your neighbor the beer fridge?