The phrase "on the grounds of [X]" means "using [X] as the reason/justification." In this case, "freedom of expression" (which Jordan has explained) is Levin's reason for defending the company's music.

I assume he means "freedom of expression" which means the ideal (protected for all US citizens in the first US constitutional amendment) that we all have the right to express our ideas and feelings even if others don't like what we have to say. Many people have protested some rap music because it may be violent, misogynistic, profane or offensive in other ways. Others respond saying that you don't have to listen to it, and the creators have the right to freedom of speech and expression.