Hi Bob - Like anything else, I'm sure there is more than one error along the way.
The "License to Purchase" - in Michigan, you need a "purchase permit" to obtain a handgun. It used to be that you had to go to your local Sheriff Dept. or LE - give them your info for a background check and they would issue you a 4 part "yellow purchase permit". Not a horrible process - usually in and out in 20 minutes or so when I did it. You then took the permit to the seller (LGS) - filled out the FFL paperwork and you got two of the four parts back - one to keep for your records and the other to return to the issuing dept. If you had a CCW permit - it was different but I wasn't familiar with that.
Now, you no longer have to go to the LE - you can go directly to the LGS, they do the FFL AND a 4 part "registration" - you get two copies and one has to be sent to the LE Dept. that used to furnish them in your county/city. A lot easier and less hassle. Primarily, the permits (registration) was to insure that the gun wasn't stolen and for future use in case it ever was from you, if recovered, it could be returned unless it was held as "evidence" in a crime.
The old method - if a person made a private sale - they still had to obtain the purchase permit only you filled it out and they ahd to return the copy to the LE. If you pulled a purchase permit the old way, and you decided not to purchase, all of the four part permit had to be returned to the issuing LE within so many days - or they would follow up to find out where it was.
In years past, I obtained some different handguns from estates, given to me, etc. that were never registered. I always registered them and they would just classify them as an "estate firearm" - run the serial # and register it. A lot of folks by-pass and by-passed getting them registered. However, if they should be stopped with a unregistered handgun - example - transporting to a range, etc. - they can be charged with "possession of an un-registered handgun" - something you don't want on your record!