If you are not an old fart like myself, you probably haven't used an actual Unix system but back in the days before the popularity of Linux, you'd see a lot of Solaris.

You stuck to your guns and didn't just lie about Unix experience, so I commend you.

But if you really want the job, next time just lie and set them straight once you've gotten an interview. It is splitting hairs to make a big deal out of actual Unix experience vs Linux experience.