Or maybe the client forwards the URL to a Microsoft service which accesses it.
If it did this, then it can forward the chat conversation as well
Exactly... ..for those who didn't get it yet, that's the main point in all this worrying about the presence of a backdoor in Skype.
but the linked page doesn't prove that it is.
It may currently be for innocent purposes (check URLs, thumbnails etc as you said). However the fact is that they can make these requests at all show that the encryption is not end-to-end, otherwise they wouldn't know the URL to make a request to at all! The request isn't being made from the client, the IP shows it comes from Microsoft's servers.
So, you're talking about voice, but this is proof that the textual chat connection that should be secure end-to-end is decrypted and routed through Microsoft's servers.