I've been through them all. I have a few pages set up, some longstanding, some new. All settings boast "Everyone", but something, somewhere must be just for some... - new pages are still fairly pristine with no apps and few sections set up.
Since I want to branch into setting up some fan pages and groups, I need to overcome this issue first.
I suspect it's a common problem since most pages I check out only "share certain information".
In the early days of FB, all seemed shared by default, then they changed policy.
Just can't find the offending setting after going through secondary, tertiary, quaternary - even quinary levels of those "security" settings.
Ruled out browser, cookie issues.
Perhaps I've turned 16 years old again ;)
Why I'd share my tax id for an answer!