BSD runs in kernel-space as well to provide the typical UNIX functionality (BSD system calls, UNIX-style processes, etc). You can see this in the kernel sources for XNU, which contains a fairly sizable chunk of a BSD kernel:

https://github.com/opensource-apple/xnu/tree/10.10/bsd

There were other projects that used comparable approaches, such as Lites:

http://www.cs.utah.edu/flux/lites/html/

No, Its a popular misconception that OSX is based on BSD... its not.

So no, this is not a misconception, it's actually true. Sure, there is BSD in userland as well, but the kernel is Mach and BSD.