The URLs are going through a couple of intermediaries. Google Chrome knows how to do that automatically. Exploder apparently doesn't.
From something I encountered at work a while back, I *THINK* the problem is that Exploder has a security-related misfeature.
If I save the image URL, and paste that directly into Exploder, Exploder pops up a dialog box asking if you really want to open this page going through that page. I conjecture that, if the URL is in the middle of a script or something like, Exploder can't/won't pop up the dialog, and just gives up on the URL.