This is, uh, disturbing! That's the last thing I'd expect. In my state, it also means that the vehicle was never listed as "salvage."
Troubling.
I haven't sold privately yet, but if I do, I'm going to insist on going to the DMV to transfer title. Title Jumping is a real problem. It can expose you to all kinds of problems. All kinds of whackos want to title jump/skip and resell your car. In most states, this is illegal.
In your case, the insurance company's indolence amounted to title jumping for you. That's terrible, and frankly you need to put a full court press on them to prove that this has been resolved in your favor. Give them a call again and make a point and get something in writing that this mixup was handled and has no impact on you.