I would have guessed the opposite - I would expect the least significant bits to have a random distribution (if the image is a photo from a camera, that is) so

I would have guessed the opposite - I would expect the least significant bits to have a random distribution (if the image is a photo from a camera, that is) so if the least significant bits of the image have a non random distribution that might be a hint that there is something hidden there. Of course, all of this is moot if the image is lossily compressed.