I was having the exact same problem.  The issue ended being that the pages were cached in IE.  I think you'll find that if you try to take advantage of any of the functionality on the page, that it looks like you're logged into, you will be forced to log in.

The problem i was having....  I would create a page that only one security role could get to.  I would.....

1. login as that role
2. navigate to that page
3. copy the URL
4. logout
5. paste the URL into my address bar
6. the page would appear in IE, but firefox would force me to log in again.

Once i was on that page in IE, if i tried to do anything, it would force me to log in.

To set your mind at ease, You can either

1. follow the steps above
2. clear IE's temp internet files between steps 4 and 5

or

1. In IE settings change check for newer versions of stored pages from "automatically" to "every time I visit the webpage"

or

1. In IE setting change disk space to use from "50" to "0"

So in other words, you are in fact logged out, its just that IE has the page cached.