That's exactly right, it wouldn't be like a cut on your face while shaving. It would be serious. This story doesn't pass muster at all.
I agree it's bogus. Looking at her arm, you can see it wasn't "written" smoothly. It looks as though the person doing it had to stop and think about each stroke.
Also, if I was going to slash somebody's face,not that I would , I think I would do vertical lines as opposed to horizontal.