At this point, she likely has a pretty good routine for screenshotting death threats. Click the notification (OSX notifies me on an OS level immediately, and I personally typically click immediately if I'm at my computer), see it's nasty, Command+Shift+4. 12 seconds is entirely doable and feasible.
I use Tweetbot as my client. When an OSX Twitter notification comes in and I click it, it takes me to Chrome, where I'm not logged in because I never use their web interface.
