The place they're talking about would be in the index.php file, so you'd have to go into the template manager and look through it to find where it is. If you didn't find it, then it's probably not in there. I didn't get that far with mine.
Question, are you trying to get rid of the favicon on the admin side or are you refreshing the actual site? The admin side will always remain the Joomla icon. Took me a while to realize that, too, so I just wonder if you're looking at your site for the refreshes or the admin side.
Also, I looked at the Shape5 website and they *do* have a favicon, that looks like a yellow ball with blue wording around it, and when I looked at the demo for the Vertex template, it was on it, too. So that means that you *can* do this. Since it's a pay template, I wasn't able to grab it and test it on my end for you. But put your favicon in one of the built-in template folders for Joomla! and switch the active template to it and see if it shows up that way. If it does, then when you switch back to the Shape5 template, it should be there. Just for fun, put a copy of the favicon in your main root directory, also.
I have gone into the template settings, but there doesn’t appear to be any favicon settings. Even If I delete the favicon completely and load it so nothing should appear I still get the Joomla icon, I am also having a problem where I delete a header banner from the template and it doesn’t get rid of it. It is like the current Joomla has its own Cache seperated from the browser as even down to the php level it is directing to the templates root folder and looking for a favicon.ico file.
The template I am using is called Vertex by Shape5.