I think it will very difficult to find a C64 with a silver Commodore badge, I believe there are only 2,000 of those C64's made. I say that because I have a first generation C64, but it has the normal badge and keyboard, but it's serial number is 2,324. It was made around November 1982, in West Germany.
I believe it's one of the first production run of machines with the rainbow stripe badge. I think the mystery might be solved if owners of silver badged and 1982 C64s posted their serial numbers, only then will we get a real estimate of how many of those machines Commodore produced.