I don't know the story, but 4.3BSD, which went into NeXTStep, was not open source. It wasn't until 4.4BSD that BSD was available without a paid Unix license.
NeXT tried to get away with a closed-source fork of GCC for Objective C, but eventually backed down under legal threat.
I think OPENSTEP for Mach 4.0, the version with the new UI that never shipped post-beta, may have been based on 4.4BSD. It wasn’t until Rhapsody that this was dusted off with bits pulled in from FreeBSD, NetBSD and OpenBSD (you can see this history in the Darwin libc source hierarchy).
The dropping of GCC and adopting LLVM is directly related to the pending switch to GPLv3 of GCC.
If there's one thing companies don't like, it's uncertainty - and the whole GPLv3 discussion gave them exactly that. They needed an alternative - and placed their bets on the more liberally licensed LLVM project.
NeXT tried to get away with a closed-source fork of GCC for Objective C, but eventually backed down under legal threat.