Agreed. If you are “always connected” IMO you aren’t too bright.
Time away is necessary.
By definition, this means unplugged.
You have to know when to turn it off.
I work for a small company, and wear many hats. Sometimes, I get a call or a email question that I can answer in seconds and save someone else hours of effort or investigation.
However, we all try to be respectful of each other's time. I'm not afraid to say "no, I don't have time until ....", for both personal reasons or other commitments at work.
When I have a day off, I typically check my work email twice a day (morning and evening). In some of the cases mentioned in the article, you aren't doing anything else anyway. Waiting at an airport is a perfect time to catch up.
However, you have to be aware of the environment. I always use secure connections (SSL, i.e. https://). The article warns against entering sensitive information on the web while using a WiFi access point, and that's just stupid: you shouldn't be entering sensitive information (including email passwords) anytime -- wired or unwired.