No - ford doesnt own ALL of mazda, just a 33.9% controlling interest. The company was founded in Japan and is still based there. Vehicles are still mostly manufactured there. It's run by the Japanese.

Volvo for example, is owned by ford technically, but they were always a swedish company, and they still build their cars in sweden, with swedish workers, and have a swedish R&D department.

Same with Jaguar, Range Rover, Land Rover etc...