The problem is that the analysis can't measure logged out accounts. Instead, they measure activity. From the article:

  ...active in this sense means the number of accounts that were 
  modified over a three-month period, including changes of avatar, 
  subscribing to a new follower or tweeting, says Guyot. 
  “We believe this is close to a monthly login rate,” he tells me. 

So they are assuming if you haven't done anything, you aren't logged in. I rarely tweet and I don't think I've ever changed my avatar. I do follow or unfollow accounts, but I'm pretty sure I could find a few three months spans in my account history where I haven't.

I generally check Twitter a couple of times a day from a logged in account, but based on the above criteria I would be considered 'inactive'.