Just stumbling around a wee bit ... bumped into a bug.
Let's say you upload a file then write a post then click 'Files...' and get the popup file manager. Let's say you tick a box then click on the 'put this into the blog post' button (but I forget what it actually says - the one that makes the groovy div img block thing). Yay for you right?
Now let's say you start at the write tab, click on 'Files...' then upload your media. The popup filemanager comes back with a green success block on top that shows the code in a text field and provides a clickable to add it to your post. That is where you will see the bug: there is a double slash before the file name, where there should only be one.
It seems that upload.ctrl.php is using $newFile->get_tag(), which in turn goes to _file.class.php and uses $this->get_url(), which in turn uses ... magic fairy dust to create an extra slash right before the image name.