The first-gen CTS actually was a German-Australian car in American clothing. Keep in mind that it was the second-gen CTS that became a true Cadi; that one fixed it all with a reworked exterior, and its aggressive design premiered the fifth-gen Camaro.
The 2003-2007 CTS is a rebadged Opel Omega / Holden Commodore. The first generation of the Sigma platform was the final iteration of the long-running V-body platform. Just like the Lincoln LS wasn't really American, but more British like the Jaguar S-Type.