BSD derived directly from AT&T UNIX. In fact, the last releases of BSD from Berkeley still contained substantial amounts of AT&T code. They made the Net/2 release without AT&T code, but this was not a complete system. 386BSD reimplemented most of the missing parts and modern BSDs built on that work.

tl;dr: while modern BSD does not contain AT&T UNIX code anymore, it evolved from AT&T UNIX. In contrast to Linux, it was not a clean-room implementation.

It's a ship of theseus.

If you replace the whole things step by step, each step a small one, is it still the same thing or isn't it?

The point is that it is not a clone of UNIX, it's one of the evolutionary strains of UNIX. You probably won't find substantial amounts of AT&T Research UNIX in Solaris, but it's still UNIX. The lineages of BSD and Solaris can be traced back directly to AT&T Research UNIX.

it seems to me that, today, this seems perhaps more a discussion of "historical context" than material reality.

after all the evolution and adaptation that's gone on over the last couple decades i wonder if saying "bsd is unix" is any more than a notional thing.

is the linux kernel materially and substantially different from any current bsd kernels?