OK, there are no real Unix systems now. That ended with SysV. However, there is a trademark for UNIX, as Perderabo points out
here. Now, whether a system can be called UNIX is no longer decided by its similarity with the original Unix, but by whether the company that sells it (Sun, HP, IBM, and so on) has the license to that trademark.
Sun, HP, IBM and others that sell UNIX have a trademark that allows them to call their product that. However, the BSD family and GNU/Linux, do not have the right to call themselves UNIX. This is why GNU/Linux is not UNIX.
This is all that I can think of.
The controversy of who owns the trademark and who owns the source is altogether different, but just a glimple:
According to my understanding, the Unix source code is owned by SCO, but the trademark is owned by The Open Group (see
www.unix.org). So, unless you license the source from SCO along with the trademark from The Open Group, you cannot use the original Unix source in your UNIX flavour!
--EDIT
Caldera (now SCO) released the original Unix source under the BSD license in 2002.
--/EDIT