Their supposed crime? To do what is most normal in any real market: insist on the right to price your own product.
Now this vital marketplace is, for all intents, under the sway of a single boss. One that has a direct interest in stripping capital from publishers. One that has a direct interest in gouging all writers who must ride its rails. One that has a direct interest in suppressing any work of reporting that questions its power, or for that matter the political economic regime that enabled such concentration of power. One that is swiftly capturing direct control over much of the rest of the U.S. economy as well.
Why is it monopolistic for six companies together with Apple to set prices, while the single company which dominates eBooks, Amazon, determine the price is fine? I have no illusions about the benevolence of Apple: were it in a dominant position, it would have as much incentive to screw over writers and publishers as Amazon does now. The structure of the agency model makes it harder for them to cudgel suppliers the way Amazon (and for that matter, the big supermarkets) currently do, but Apple has already shown a willingness to ban content it finds objectionable, and considers it a public service.
The real problem is that the eBook market is immature, and like all new markets is vulnerable to domination by the early entrants. The same thing happened in computers, phones, railways, and oil, to name but a few examples. Markets do not work without competition; they become an excuse for the dominant player to extract tribute from everyone else. That was the point of anti-trust laws in the first place, yet this suit will end up making the situation even worse.