If you write a song and someone rips you off, you want justice. If someone lifts pieces of a song you've written without permission for their own purposes, you want compensation. But what if someone just copies your style? Is that grounds for a lawsuit?
The Black Keys certainly think so. They believe that their signature style--the sounds and audio aesthetics that make them sound like they do--has been, er, appropriated unlawfully.
This is the world of "soundalikes." Radio and other production libraries along with agencies and music supervisors will often commission a piece of music to sound similar to a well-known song. The trick is to change the arrangement just enough so that while its legally distinct, it still evokes the memory and/or feeling of the famous song it's aping.
This has been going on forever on radio, TV and in movies. And none of this is illegal. The Black Keys would beg to differ. They believe that a style of playing can be protected in the same way a song can. It's part of their style which deserves to be protected as much as anything they do from thieves.
This is over the top but they might win. There have been precedents in the acting world.
The main issue is can the Black Keys argue that their sound is unique or did they copy others. The answer is surely they copied others in style.
I also think there will be a rash of lawsuits after this as there are plenty of bands that sound similar to another.