It was everything they were sampling in 1986, and more. And less.
Pop music was definitely on a downturn in 1985-1986 though, after the heights of 1983-1984. But I'd argue that the downturn continued until about 1992, when "alternative" became mainstream. (duriyah
will disagree about that part though.)
The Beastie Boys started as part of the growing mainstreaming of rap, coming out around the same time that Run-DMC redid "Walk This Way" on their breakthrough Raising Hell album. That album is right beside Licensed To Ill in my memory of the time.
(Aside: I just recently heard (possibly on Sound Opinions
that "Fight For Your Right" was basically intended as a slam against the very people who loved that song, and nobody really understood that.)
I really need to listen to "Paul's Boutique" sometime.