These people tend to view "checking their email" as something akind to social media, if it's their private email. They also tend to use a few different email-adresses, so she might be checking her "work" email, and seeing if anything caught fire while she was asleep. All of my bosses have done this very openly, though that might be more of a thing in lawfirms, since the partners who run these things tend to be old as hell and terrible with anything more technologically complicated than Microsoft Word.