My best guess right now, due to testing with other sources, is that for some reason this is specific to Turbine's web server. Whether this is intentional or otherwise - I'm not sure, but regardless, it needs to be solved.
As far as I'm concerned, the best option I have at my disposal is to simply copy every single icon over to my server, and then load it from there. Anyway, I'll keep everybody posted - I will try to make this as seamless as possible, so hopefully you won't have to check back here just to see if it's working
In the middle of downloading & copying over the icons - this will probably take quite a while, but hopefully sometime today you should start seeing real icons instead of the black squares.
Final Update - for now
You should start seeing real icons after the first time it updates, if you want to cut to the chase, just close and reopen it.