I don’t really think it’s meant to be a tribute as much as an extrapolation on the song’s theme. Heems is commenting on how the song was originally removed from the American version of the album due to nationalist, political sentiments after 9/11, and pointing out that though a band of rich white kids could more conveniently put their complaints with NYC police aside for the moment, those from minority communities couldn’t possibly ignore the abuses of the police.
So yeah, it resembles the original mostly just in theme I think. The sample, I agree, is eh. It’s a broad definition of cover, but, hey, I’d rather have interesting material and honest artistic reinterpretations anyway.