Someone in the DMV office lied to you or you didn't explain the situation correctly.
In '68 you'd have a transferable registration as proof of ownership. There is no title. You can hold this registration without plates. Only if you're plating it do you have to have insurance on it. You tell the DMV that you're transferring the registration into your name as proof of ownership and you're not putting it on the road. At that point, you'll be given a registration with the plate number section left blank.
As a matter of fact, that's one of the things my local DMV usually asks. "Are you transferring this as proof of ownership or are you putting the car on the road?"