This argument is a cousin of the trademark claim that the Supreme Court killed off in Dastar v. Twentieth Century Fox. The band apparently reframes its argument in the language of publicity rights (Guitar Hero has mis-appropriated the “likeness” of the band via reproducing its distinctive sound), and therefore tries to thread the needle arguably left intact, post-Dastar, in cases like Wendt v. Host International. Like the claim in Dastar, it deserves to die the special death reserved for mutant copyright.
The producers of Guitar Hero procured a license to record the cover by following the requirements of Section 115 of the Copyright Act:
A compulsory license includes the privilege of making a musical arrangement of the work to the extent necessary to conform it to the style or manner of interpretation of the performance involved, but the arrangement shall not change the basic melody or fundamental character of the work, and shall not be subject to protection as a derivative work under this title, except with the express consent of the copyright owner.
Got that? If you re-record the properly licensed tune and it doesn't sound more or less the same as the original, they can sue you. And if it sounds too much like the original, they're gonna sue you too. Dear Romantics: I've played that song in public thousands of times myself. It's wedding band fodder and football game timeout background music at this point. I could play it on any instrument, and sing all the parts, too. I could teach four or five gradeschoolers to play it exactly like the record in a week, even if they had never played music before. You guys should cash the publishing check, be glad anyone's paying attention to you anymore, and go back to watching Matlock in the Nursing Home.