The rules state not to make a fan game/demake, etc. "It's simple. No copyright violation!"

From a music perspective - would Game Boy covers of popular music be permitted as background music? A famous rock song, for instance?

(I'm okay with the answer either way.)

If there is still a copyright owner, no.
Old classic music for example would usually be fine.
Rock music might not be in most cases.

*I simply don't want to encourage people to do any kind of copyright violation.

Thank you for the clarification!