If I understand what they're saying (I'm not quite sure either), Facebook basically does a Man in the Middle Attack when you click a link that allows them to see what you click on after leaving their page?

On the one hand, it sounds crazy, but on the other it doesn't sound outside the realm of possibility based on other things they supposedly do like create shadow accounts of people you and other people know/talk about to build a data profile on them and people they may know so that if they create an account, Facebook already knows what people are in their area and likely in their social circles (and the stuff that they actually do right out in the open where it's obvious).

Still irrelevant to the issue anyway, but weird to think about. More to the point at hand, I wonder if your issue is caused by Facebook opening the picture in some kind of container instead of the actual page/link itself, like how Reddit opens images on the Reddit page when you try to open them directly - it won't let you view the image as a source file if you try to open it from a search engine.