Regarding the year on the title vs the "model year" my experience in troubleshooting problems led me to realize that in general "model years" were not significant to either the car manufacturers or licensing people from the 1900's into the mid 1920's. The "year" on the title/regestration was the first year the vehicle was registered, regardless of when built.
Then as car manufacturing evolved and marketing became more important the "model year" became more important. Partially from a tax standpoint but also as a protection of value for the owner of the vehicle and affected people such as insurance carriers and potential purchasers. So the various states (remember, each state can be quasi-independent on their licensing rules, uniformity is generally by agreement of the states) responded to the public need by attempting to reflect the model year on the vehicles paperwork. This did not happen all at once.
My belief is that some states (particularly North Dakota) did not get around to the "model year" scheme until the early 1930's. We and a customer had a mutually frustrating experience with a large shipment of parts for a "1934" pickup. Nothing fit. After trading photos and some research on my customers effort we figured out that this was an unsold 1931 (depression, remember) that did not leave the dealers lot until 1934.
Back to the original discussion, could a 1930 or 1931 legitimately be titled as a 1932... yes. Was that particular car originally built with a 1932 frame... The only ones who might believe that are the ones who would believe a burnt out hulk of a common tudor sedan body on a mediocre street rod chassis are worth 14K.