Players have already decided, that they don't want their families, girlfriends there that speaks volume to the amount of fear they and a lot of fans are having.
I dunno that it shows they're trembling with fear, just, well..."Honey? You and the kids might die. So you should probably stay home." From a you-don't-want-your-family-to-die perspective, it's a no-brainer. And, less nobly, you'd rather not have concerns about your family's safety in the back (or front) of your mind while competing for Olympic Gold. And, honestly, families can be kind of annoying.