I quit reading when it said 'bought same day as produced', that told me everything I need to know to run away.
The odd thing is that it's possible. In those days, you could buy off the lot or get it with a special order. If someone wanted certain options, and a "K" code was an option, you would most likely have to special order it. This one could have had a customer that wanted a "K" code and bingo! The dealer found one. This car's VIN is in the range of the 23rd of November, 1965, so if the buyer put a down payment on that date, the car was his. The actual delivery date is whole different situation. The registration date is also a different situation. There is also the "scheduled" build date and the "actual" build date may have been as much as two to four weeks different.
Bottom line is - it's possible, although not likely.
The e-bay listing has more pictures that "appeared" including several of the engine compartment. The prominent discrepancies there are the incorrect fuel pump, coil mounted on the intake and non-painted shock towers and firewall braces. There are a couple of pictures of the VIN on the block and transmission.