The in-game usage of the band is similar to the way music celebrities were used in Guitar Hero 5, and it allows the members of No Doubt, along with Taylor Swift and Adam Levine from Maroon 5 to appear in any role on any of the game's songs. You... may also remember that this is the exact same scenario that caused all of the uproar over the way Kurt Cobain's likeness was treated in that game, which led to a lot of Twitter-based unpleasantness from Courtney Love and, really, a lot of negative feelings from a lot of different people.
The LA Times article on the topic says that the ability to make Gwen Stefani sing "Honky Tonk Women" by the Rolling Stones is a specific sore spot. Like this:
Well, when you put it that way, maybe they've got a point. The suit also claims that the band's request to limit their usage specifically to their own songs was turned down because it would be "too expensive" to patch it.
“While No Doubt are avid fans of the Rolling Stones and even have performed in concerts with the Rolling Stones,” the complaint states, “the Character Manipulation Feature results in an unauthorized performance by the Gwen Stefani avatar in a male voice boasting about having sex with prostitutes.”
Activision's issued a statement in response to the suit, so here's a bit of that:
It sounds like someone, somewhere needed to spend more time reading the fine print, but after the double-whammy of Kurt Cobain and No Doubt, I'm going to guess that this process of using likenesses in rhythm games will either get a lot more formal and specific or Activision will just do away with it entirely and save the likenesses for band-specific products, rather than attempting to cram them in alongside the standard cast of the Guitar Hero franchise and be forced to enact a bunch of specific limits on usage. It's probably not worth it for the company to negotiate likeness rights if they can only use them for two or three songs. Be sure to read the LA Times article for more of the back and forth between the two camps.
“Some of the world’s most popular and iconic artists have been featured in Guitar Hero as playable characters, and we are proud to count No Doubt among them,” Activision’s statement said. “Activision has a written agreement to use No Doubt in Band Hero – an agreement signed by No Doubt after extensive negotiations with its representatives, who collectively have decades of experience in the entertainment industry. Pursuant to that agreement, Activision worked with No Doubt and the band’s management in developing Band Hero…. Activision is exploring its own legal options with respect to No Doubt’s obligations under the agreement.”