I don't believe there would be any way of correcting the record short of suit to Quiet Title.
The validity of any other method of striking the assignment would be an issue of title, in the event the property were to be sold or refinanced. So, if we look at what the Title Company would find acceptable to clear the item off of title, it would look to how the assignment was deemed invalid. Even with your analysis of how an entity cannot make an assignment unless it has an interest to assign, you still need an authority greater than mere logic to satisfy the Title Company. I would think that only a Court Order would suffice - unless the creditor voluntarily filed an affidavit of error with the Recorder of Deeds.
This answer does not constitute legal advice and does not and is not intended to create an attorney-client relationship. The law may vary depending on the state in which you reside. It is intended only to give some direction in which to seek assistance.