It is a rather difficult question to answer and it seems that both automakers have their answers or versions to it. An image of a slide (pictured below) stating the development phase of the car has been going around the internet recently; starting from the product planning stage up to the evaluation stage. This image is rumoured to be from Toyota Motor Corporation.
But if you were to take a look closely at the car, you would notice that the engine is purely Subaru as it is a boxer engine. Based on the latest FB engine series, the high-revving engine delivers around 200bhp and 205NM of torque and the D4-S direct injection system is Toyota's most obvious contribution to the engine and drivetrain.
And what about the other engineering parts of the car? It is known that the platform is an entirely new one and it is said that the suspension design is based on that of an Impreza. Subaru previously has mentioned that the spring rates in both cars are different. The BRZ has a stiffer front while the 86 is stiffer at the rear. But the difference was said to be rather minimal and most people won’t feel or know the difference.
In short, it seems that the idea for the car was conjured up by Toyota and they acquired the assistance of Subaru for some of the engineering parts. Regardless of whoever owns the rights to it and whichever marque we choose, I am just glad that both companies have co-develop something that is lacking in Japanese cars (especially in these two companies’ model line-up) nowadays and that is a nice looking coupe.