The 360 has the highest games-to-console attach rate of any system ever. If repeat buyers are a significant portion of 360 sales then the 360's attach rate would be absolutely insane. Therefore it's easy to reason that broken consoles make up a very small percentage of total units sold.
I don't follow the video game industry at all, so forgive my ignorance. After looking up 'attach rate', I'm not sure I agree with you, though I do believe I follow your logic.