Millions of people have a work e-mail address. Most of them don't use it for personal correspondence, and don't need the distinction to be explained to them. They also don't do company business from their personal gmail accounts.
I listen all the over the web and don't remember my source. It's almost worse if he DID recommend she use one for personal use and she didn't get it that the purpose is to keep personal and business separate... Or chose to ignore it on purpose--shows bad intent.