It's the other way around, actually: by law in the US and most countries worldwide, suppliers are free to set whatever prices and terms they like, but retailers have the final authority to set the price that's presented to the retail customer. Suppliers can not unilaterally dictate to retailers the final sales price the retail customer pays.

That's why "Manufacturer's Suggested Retail Price" (usually abbreviated MRSP) is a thing. The manufacturer / supplier suggests a price, but the retailer makes the final call. The only recourse suppliers have to this is pulling distribution from that retailer entirely, as long as they apply the same policy to all retailers - companies like Apple and Bose make credible threats to do this to suppliers that violate their guidelines, which is why their prices are so consistent across retailers.

Otherwise, retailers have the final call on retail pricing unless they waive that right via negotiation: if they want to sell at a loss, or reduce their own margin to use lower prices as a marketing tool, they can. That's why Walmart and Target often sell bottles of Tide below cost - it's called a "loss leader" strategy, and it's very common as a way to attract new business.

Amazon used loss leader pricing on bestselling titles to establish the Kindle platform, which is a major reason why it's the dominant ebook platform now.

A big part of this dispute is that Hachette is demanding final authority on setting prices, and demanding that Amazon gives up the right to discount and use its ebooks as loss leaders - instead, they'd get a flat percentage (likely ~30%) of whatever Hachette decides to charge. This is a major part of what's now called "agency pricing," and the big 5 publishers and Apple colluded to force Amazon to adopt it several years ago. That's why the DOJ filed suit for antitrust / collusion / price fixing, and the publishers each lost or chose to settle.

As a condition of the judgement / settlement, publishers now have to renegotiate their contracts with Amazon. Amazon, justifiably, isn't willing to agree to agency pricing without major concessions. Hachette won't agree to standard retail non-agency pricing. Hence the impasse.

EDIT: also to clarify, wholesale non-agency pricing isn't "unprecedented in the book business." Barnes & Noble and independent retailers have operated on wholesale pricing for print books for decades. Otherwise, B&N wouldn't be able to place a "20% off" sticker on bestselling titles, or offer large discounts to move remaindered stock. Hachette is asking Amazon to agree to something no other book retailer has or would agree to. Retailers like Apple and B&N/Nook have agreed to agency pricing on ebooks in the hopes of shutting down Amazon's ability to discount, with the understanding that publishers were attempting to force Amazon to do the same. (Via collusion.)

The larger game is that Hachette (and other large publishers) are attempting to protect their hardcover print sales by inflating the price of ebooks, which makes them less attractive to readers. Ebooks are more profitable, but it's a more difficult market to control, so publishers are fighting Amazon and doing what they can to slow ebook adoption as much as possible. It's not a smart strategy, IMO, but that's what they're doing.