(I'm pretty sure the way it works is: it shows the image for certain referrers, and when you load the "full" page it requests the image with a referrer of imgur. That way you get the image, and then subsequent requests to the image are served from your browser cache so the direct links work)
Anyway, thanks for expanding on it; I've shared a few images through imgur and never had this issue (maybe it was before this change, or maybe the people receiving them never complained), so I was a bit puzzled by your comment.
... aaaaand now I want to make a malicious image host that always shows you your uploaded images but serves up goatse to anyone you link it to. Or maybe just flips the images, upsidedownternet style.