Keep an eye on http://opensource.apple.com
Yes, the foundation (core OS components, kernel, libc and more) of both OSX and iOS comes from BSD, and unlike GPL, BSD licenses do not require anyone to release the modifications, meaning that Apple can bring BSD code into their systems without publishing anything - typically BSD licenses require you to mention that BSD code is used. Both OSX and iOS also have GPL and LGPL components and a lot more. On your iOS device, go to Settings-General-About-Rights and Juridic information (or something like that, I'm on Norwegian settings), and you see all relevant licenses, copyrights etc for various components used in iOS, quite a few of them showing the legacy back to NeXTStep, which was for most part BSD too.
It is fully possible to configure an OSX box to not boot into the "Mac interface", and instead boot into X.org and a display manager, just like any other BSD or Linux distro, and if anyone is interested in installing Darwin without the "OSX fluff", that is possible too:
Originally Posted by Vot
I think he is referring to the large potions of bsd that apple used.