I think we're disconnected on this because my point is that branding Yahoo results pages with the Bing logo is horrible for Yahoo.

And yes, while luxury brands use many parts not specifically made by them, they do not promote another brand who is a competitor.

Another analogy maybe? If the Apple iPhone had a splash screen that said "Powered by Microsoft" it would harm the brand. Apple knows this and while my mac is powered by Intel, there's never any "Intel Inside" branding.