the arrangement between apple & apple is basically that the computer maker can't brand music enterprises. itunes has been a sore spot already, so i can't imagine apple (computer) pressing their luck, especially in this situation that appears to be cut-and-dried.
I agree with the previous guys. Apple Computer cannot sue Apple Records because Apple Computer was the one that infringed into their trademark. It was founded by the Beatles in 1968. Apple Computer was started in the late 1970's. They both reached an out-of-court agreement to keep out of each other's business. Apple Computer violated that agreement when it started Itunes store and started selling music, so they went back and made a new deal.
On 5 February 2007, Apple Inc. and Apple Corps announced a settlement of their trademark dispute under which Apple Inc. will own all of the trademarks related to “Apple” (including all designs of the famed 'Granny Smith' Apple Corps Ltd. logos) and will license certain of those trademarks back to Apple Corps for their continued use. The settlement ends the ongoing trademark lawsuit between the companies, with each party bearing its own legal costs, and Apple Inc. will continue using its name and logos on iTunes. The settlement includes terms that are confidential