I've been selling on Amazon for years, have had a 100% positive feedback rating from the very beginning... no negative EVER. I've switched to Fulfillment by Amazon recently. I'm the publisher of the book in question (the Original Green) and have the low price. Yet a company that only lists them used, and at a higher price, and a lower positive rating, wins the Buy Box. Because they're listed as Used, customers have been complaining to me that Amazon isn't selling any new books, and they don't want used ones. So we're losing sales.
After I got off the phone with the completely unhelpful agent, I've been Googling, and it turns out that there are known factors in winning the Buy Box. For example, it appears that you have to be a Gold Level merchant to qualify, according to one site. He could have told me that, and could have told me how to become a Gold Level merchant. And it appears that while the exact algorithm is a closely guarded secret, there are enough factors that Amazon has revealed that a seller can, if properly instructed by Amazon, increase their chances of winning the Buy Box. The agent's approach of saying that "there's nothing you can possibly know about winning the Buy Box" is counter-productive for everyone involved. Give people a target, and they may shoot for it (and help Amazon in the process.) Hide the target in the dark, and nobody wins.
One other thing I've learned, which is a big help, assuming people get to the book using my link: If you go to the master listing for the Original Green book, you'll see the Used seller in the Buy Box. But then, I tried an experiment: I went first to my Amazon storefront, then clicked on the Original Green book there. It took me to a different Original Green listing page, showing only me as the seller. And it had a perfectly normal (large) Add to Cart button where you'd expect it. I guess I'll have to rebuild all my links to my stuff to these detail pages.