It sounds like they are taxing you on the "fair market value" rather than the purchase price. That has become increasingly common in states with personal property taxes on vehicles, probably because people had learned to scam the taxman with phony purchase orders or other ways to show an artificially low price.
And they get to calculate the "market value"! Is there perhaps an appeal p[rocess where you could demonstrate that the state's "market value" is not realistic? It would probably take more than just one purchase contract to show that, however.
2004 American Tradition; 2014 Buick LaCRosse
Homebase in the Ocala Nat'l Forest near Ocala, FL