and hence, the word insurance is oh so important!
You've hit the nail on the head. Human error is one of the two huge reasons for buying title insurance. The other huge reason is theft by fraud.
So, you order title insurance. What happens next? The title insurer has an abstract of title performed either by machine or by an experienced human. The abstract will likely be reviewed by an experienced human examiner who reviews the abstract for accuracy and makes decisions about insurability. The examiner will prepare your title insurance commitment.
If your title company uses fully automated title, they will skip this step and just spit out the poop from the garbage in garbage out machine and plop it electronically into a title insurance commitment form. The poop just plops out and populates all the fields of that form. [Can you tell I don't like fully automated title?]
BTW - Which form of title examination would you prefer? Experienced human professional examiner or plopped out poop from a machine? Human? Good answer - now remember that when you are shopping for title insurance. Ask your title agent if THEY prepare the title commitment or does it come electronically and just plop into their system. If your title agent does not have the expertise to prepare a title commitment, you don't want them messing around with your transaction. They are likely profiteers in the business for a buck and have no professional interest in the honorable profession of land conveyance. Trust me, you want someone who really cares about good title.
So, if the abstractor makes an error and does not find a lien, the title INSURANCE will cover you. If there was no chance of an error, you wouldn't pay for insurance, you'd just pay for a search.