I had something very similar a few years ago. I'd create a new file on my server that no one could possibly know about, then look at it in my browser, and within a minute or two I'd see in cPanel > Latest Visitors that a mysterious IP had also fetched the file.
It turned out that my antivirus program was intercepting my browser requests and sending the URLs to the AV company. The company fetched the file from their own IPs (there were a bunch of them), and presumably checked it for viruses.
They still do it, but I've just gotten used to it.
If I really want a file to be inaccessible/secret, I must put it behind password protection, even if it will only be on the server for a few seconds.
Maybe BlueCoat offers a browser security service similar to that, and you or someone who does know about your file is using that AV product, or browser extension, or whatever.
whereas blue coat just get the HTTP/etc, and nothing else! What's with that?
Anyone who gets the 403 won't load the auxilliary CSS, JS, files, etc. because the 403 page probably doesn't have the links to them that the real page has. That might not actually be what you were asking about, though(?)