Nonsense? What? Why?
OK... forget the specific edit_post_link() issue. It's the same problem as the login/out.
You are in the WP directory, and you login. THEN, you go to the Home page of my website, outside of WP. The Home page uses the WP loop to display recent posts or whatever, and on the Home page I need it to still display that you are logged in, but it doesn't.
It doesn't know you're logged in anymore and so you are effectively logged out. Therefore, the posts on the Home page don't display the edit_post_link() that I have put in them, because you're not logged in.
If I click on a post, which takes me to a single.php (back in WP) it will show me as logged in. If I go back to the Home page... no longer logged in. And so on.
If I put a loginout() link on the Home page, I can log in but it will be like a separate login. I am logged in to the home page, and the WP system as the same person, at the same time, but completely separately and they have no knowledge of each other.
How is that nonsense? Has nobody ever wanted the website to display you as logged in EVERYWHERE, even outside of WP? If I am including wp-blog-header.php, I thought maybe it would still know I'm logged in.