Yesterday we were leaving for a picnic. I logged out before we left. I got to the page that said that all cookies were cleared, etc. and my husband told me to hurry up, so I closed the browser and hurried downstairs.

This morning I was still logged in. Are you required to actually leave that page in order to be logged out?

No, you're not. Your username still shows up on that one page, but after that you should be completely logged out, whether you then go somewhere else on the site or not. I've no idea why you would have ended up still logged in; I used the logout feature a couple of days ago and it worked fine, so I suspect it's probably a fluke.