I've been searching for the forums on this topic and there doesn't seem to be much of an update over the last few months.
It seems like the only way to turn off global tags is to cheat the system by marking your blog as mature content. As recommended here: http://en.forums.wordpress.com/topic.php?id=9298
However, I'm pretty sure that will have bad side effects, so I'm trying to stay away from using that technique.
I wouldn't mind the global tags, if it wasn't so confusing. Right now, when a user clicks on a category at the bottom of my post, it shows global posts. But if they click on the same tag in my sidebar, then they see only my posts.
I've ended up adding my own links to the bottom of my posts that link to my categories, but the global tags are still there. So now, I just have 2 sets of links on the bottom of my posts - which is not the best way of doing it.
I also know that I can turn off the setting under Privacy, but that limits your visibility to search engines as well. Seems like it would be nice to have a checkbox under Presentation/Extras, just like the Snap Preview option.
But, I'd rather just have the themes edited to say that the links are GLOBAL and not linking to my own blog. Its just too confusing for me and anyone who expects the link to be site-specific navigation. Or even better, what about all of the themes having 2 sets of links. One local and one global?
Original request was closed by admin a long time ago: