There is different browsers and so on....
quick look I did found this
You could try the following
Set the Logout URL as
Create page 999 with no regions
In the Security section set Authentication to 'Page is Public'
I tried that and it is working fine for me too.
I needed to navigate to an external website when pressing a botton
So I used your method to acheive it
However - once you navigated to that website you cannot go 'back' to your appex application
How do I make the new website open a new browser window ?