Originally, an 'American Car' was easy to spot.
Ford
Chevrolet
General Motors
In the global marketplace, design and engineering are quite blurry now. Japanese manufacturers open production plants in the United States, and the American designers depend on European and Asian parts.
Your Toyota Camry may have been built in Kansas.
Manufacturers are changing owners. Ford assimilated Jaguar. Mercedes Benz and Jeep automobiles are made by the hybrid Daimler Chrysler Corporation.
One example of a shared design is the Mitsubishi Eclipse. The Jeep/Eagle Talon and Plymouth Laser are essentially the same car.
Another example of "shared design" in cars is the Dodge Stealth and Mitsubishi 3000 GT. The Mitsubishi folks created the innards, while Dodge focused on the body styling. Mitsubishi then altered the body design to make it a bit more aggressive-looking, and bumped up the power and features of the Mitsubishi 3000 GT VR-4. Detroit hails the Stealth as an American design triumph.
Truly, there's no such thing as a purely American Car anymore.