To add to the above post, it's my opinion that Honda should be shouting from the rooftops that they have a Cosworth engine in their supercar. It would give the press something to talk about and add to the mystique of the car. Toyota / Lexus was not embarrassed to do this with the Yamaha-developed V10 in the LFA, and the Cosworth name is arguably much more impressive than Yamaha.
Of course, we all love Honda for their in-house developed engines. But, the reality is Honda was known for N/A high-revving engines, which they went away from on this NSX and in their current lineup across the board. I don't think anyone hears "Honda engine" and pictures a twin-turbocharged V6 that can reach peak power at 6,500 RPM, so I find the premise that the current engine being built in-house would somehow improve the perception of the car doubtful.