OK, I have just created a new PS3 test store, and looked at the code for the logos there, and the code is different this time to the code in my real store.
What has basically happened is that the installation process on my local testing server has created this path:
Where as on the remote live server, it has created this:
So, it would seem that there are more differences between a live and testing server than initially meets the eye, but this isn't too big of a deal. I just don't understand why the logo doesn't work when the files displaying them are at the same level as the Images folder meaning that they are relative to the logo's position. Why has the local installation added the extra /~username/PS3test/ when the site root is inside the folder of PS3test? It's basically the same as the remote installation isn't it?