No, they didn't tax based on current value although they considered it for awhile hence the $1200/yr registration fee being thrown around momentarily. The key was that it be classified as a 1965 car rather than a new car. If it was a new car then the fee would have been $1200, but they were nice enough to classify it as a 1965 and thus get the $40/year rate. We had all the invoices and they looked at them but evidently the computer values the car as if it were new in 1965 then depreciates the value over 43 years in this case and comes up with the registration fee -- $40/yr. which I think is a minimum.
BTW I took a video of the car after we got back from getting the title. What you can't see is it's 108 degrees outside and we just finished a, ahem, "spirited" 10 mile run down the freeway then some stop and go traffic to get back to the shop. I overheated but the engine didn't - stayed nice and cool, unlike me. The engine had been shut down for just a minute after the run when this video was taken and may have something to do with why it looks like it's starting rich.