Inquiry:
I was wondering about this 63 Avanti in Houston: http://www.northfreewayhyundai.com/used-Houston-1963-Studebaker-Avanti-Base-0000000001A043016
I've been in touch with the agent there, Tony Zwigart, about the VIN listed on the title. He said that was the VIN given to the car by the DMV in the state where one of the previous owners lived.
According to Tony, the actual VIN (or at least the stainless steel plate on the frame) is R4415. I'll also attach a picture below of the body number plate (RQ3294).
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Response:

 I also inquired about the VIN on this car (for data purposes) and perhaps the agent had me confused with you.  After not receiving a reply thru Ebay,  went to the dealership's site and contacted the President of the company asking if my request could be satisfied.   His reply to me was that (quote) "I thought Tony got you the VIN" (unquote).
   It was also explained that the new VIN was issued because the actual chassis plate was not available and the previous owner couldn't find it..  In order to get the car registered, the DMV had to assign a new number...

    So this entire thing about the VIN gave me a few sinister thoughts, but if he actually does HAVE the factory frame plate, then why wasn't it used in the registration.    There would be a way to verify the numbers, but it would cost around $40.00 for the Studebaker Museum to look up the body number and find the actual build sheet.  The build sheet would show the chassis number, body number, engine number, etc.
 
Unfortunately, buying a car long distance is not the best way to proceed without having someone inspect the car.    The pictures show a lot of good points, but I'd be interested in a couple others, like the steel torque boxes that span the wheel wells and tie the fiberglass body to the frame.   If these are rusted enough, the integrity of the car is compromised and they are expensive to fix.  Having someone test drive the car to check the engine would also be recommended.

At any rate, the car "looks" to be fairly nice. You might notice that the exhaust headers are the R3 style, a nice addition.  Also the upgraded dual circuit master cylinder.   R-4415 was built in May of 1963 and is not a transition car.  Those cars  started around R-4700.  In fact, most all the running changes began after R-4420, however this car has the upgraded upholstery.  There is one glitch in this car that stands out, in that the battery is NOT the long 3EE type, rather the group 24 type.  This change wasn't effected until R-4892, so that needs an explanation.  Note that the engine compartment is bright and clean.  A car with 83K miles would not look like this, even if it was maintained meticulously.     The cars with the group 24 battery have a different design inner fender, so you cannot just change the battery out, this required body work.   Why would someone go to that length to change the battery style, except perhaps an accident required the panels to be repaired and the old inner fenders were no longer available...   shiny engine bay, different battery panel....  adds up to repair work in my mind.  Just speculation though , but there's much more of a story to this car than  is being told.   I can't see anything in the photos  underneath that would indicate damage however.   There are other things that stand out, but not detrimental.

So I hope that this point of view was meaningful.  Again, you should never purchase a car sight unseen.