I inherited a Druapl5 site and it's showing content when published is not checked in the Publishing Options section of the Edit Content Form.
I confirmed that the status is 0 in the DB for the node. So it should be not visible.
My first guess was that I was logged in and that's why I could see it, but I logged out and I could still see it. I tried a different browser and the same thing so it's not that.
Also, the unpublished nodes are coming up in the search results which I originally thought was an out of date search cache, but may be something different.
Ever seen anything like this? Any ideas?
You mentioned in a comment that Content Access is installed on the site. This module (as well as several others, e.g. ACL) overrides the default Drupal node access mechanism in order to provide additional/more fine grained permission settings.
So my guess is that the permission configurations in that Module are configured wrong for your desired results. As far as I recall, it allows separate permission sets per content type (defined for authors and roles). You should look at your content type edit/definition pages - there should be a tab added by that module to configure the permissions. Also check the readme.txt of the module, as it might give some additional hints.
If that does not help, you should check if other node access modules are installed as well. As mentioned, there are quite a few of them, and their interactions are not easy to determine (One should aim to use only one, if possible).