Yeah, when I lived in SoCal, it was the CHP that knew what was going on as far as VIN verification was concerned. I'm surprised, however, that the DMV is that clueless.
... Well, maybe not...
Seriously, you might want to talk to a supervisor. It might be that the 13 digit VIN threw her off (all cars since 1981 have had a 17 digit VIN) but there are enough old cars on the road in Calif that the DMV OUGHT to understand this.
Now that I think about it, when I moved to CA in 1980, they did send someone out to look at my car (a 72 442, by the way) and verify the VIN. I seem to recall that the person was a CHP officer assigned to the DMV for this very purpose.
62 F-85 Deluxe wagon (the NV desert car)
62 F-85 Deluxe wagon (the San Jose car)
64 Vista Cruiser
64 Jetstar 88 Conv
66 442 L-69 Conv
84 Custom Cruiser
86 Caprice wagon (w/307 Olds)