I read this post yesterday and this specific example kept coming back to me because something about it just didn't sit right. And I finally figured it out: Glancing at the alert box (or the browser-provided "do you want to navigate away from this page" modal) and considering the text that I had entered takes... less than 5 seconds.
Sure, 5 seconds here and there adds up over the course of a day, but I really feel like this example is grasping at straws.