You simply haven't solved the major problem here, which is one of discoverability and easy, decentralized lookup.
"So, you're claiming that this bike, which has a frame number that matches the one reported stolen, is in fact a different bike with the same frame number, one on which both producers neglected to brand in any way shape or form, and that you have no record of purchasing..."
And if uniqueness is somehow important, then the idea of local governments having some registry is just as bad. My road bike would have four of these silly municipal numbers on them from four different municipalities, about to be five. I can't imagine that this number is any more unique amongst municipalities as it is amongst vendors.