For most 65s it will be visible on the engine compartment sheet metal in front of the shock tower. There should be a fender cutout. There are often two "hidden" VINs also in the engine compartment. Basically they are under the fender lip behind the shock towers, about the same distance back, as the visible one is forward of the tower. You can sometimse loosen the fender bolts and lift the fender and see these. On some cars the hidden VIN is only on one side. I think the different manufacturing plants used had different policies.
If it is an original K code car the vin is also sometimes on the engine block and tranny tailshaft. Some have claimed that for a K code it is also inside the the rear frame rails somewhere - I've never had a K code and don't know about this.
While there was a VIN stamped on the original door plate, the door or plate could have been changed. Hence the message on the door plate that it is not a legal VIN record.