It's when the phrase is at or near generalization that it comes into play - someone searching for Kleenex likely doesn't care what tissue they find, and many people who Google Google would be happy to click Bing if it popped up first.

"Dominos" might be one where people wouldn't mind ordering from Pizza Hut as they're using it as a generic term for pizza.

I'm quite certain brand confusion is entirely the result of a poor advertising system that allows it.