I fixed it. It's Picasa trying to prevent hotlinking with their weird URLs. Anything over 800 pixels is what appears to be the problem. If you limit the pic to certian sizes, they will work.
Example: take the URL of the pic:
And change the s912 part to one of these sizes 200, 288, 320, 400, 512, 576, 640, 720, or 800 :
and it should work.