The photo that is provided is not necessarily the image that the judges used to place the horse.
As was pointed out, the camera takes thousands of images per second at a stationary target, essentially the plane along which the mirror lies, which ought to be the wire.
That image is captured in its entirety on a high-res computer screen which can be magnified to such a degree that under normal circumstances, you could tell what color eyes the jock has through a set of goggles.
The person that creates the image that the public views is charged with doing several things in producing an image, one of which is to create an image that gives the best overall picture in terms of relativity.
That person is also usually supposed to be somewhat "artistic", insofar that they are expected to produce a picture that not only demonstrates the relative positions, but does so in an aesthetically pleasing manner. Clearly, this is not the priority if the two are mutually exclusive, so ordinarily in a case like this - one would choose to provide a photo like the one seen above and then hopefully, a more magnified photo of the same two so that there is no doubt that the magnified version is in fact the same image as the one seen at "less magnification".
The photo finish camera, unless it has been somehow tampered with, which is unlikely to say the least since most are stabilized to precision - is as close to infallible as it gets. The margin for error generally lies with those that read the image, but it is fairly difficult to misread an image with the incredible technology at one's hands.
Mistakes do happen, I'm sure - but the old stories about blown photos are a thing of the past with what is used today.
One of my favorite things to do is to invite people - bettors, horsemen, whoever - to watch a race upstairs and view the mechanics of the photo finish camera and the placings. The most grizzled veteran is amazed the first time that he/she sees it in action and usually will join the alliance of those that have faith in the camera and the computer.
The camera uses software that creates images that I can't view without the actual software, otherwise I would provide an example of a "race". That is what you see when you look at the image - the entire race on a lateral slide, with every horse's relative position and a perpendicular line that can be placed anywhere on the overall image created - but remember - the actual "photo" is only being taken on a straight plane to the wire.
It is a somewhat difficult concept to visualize if you can't see it so imagine the following:
You sit on the side of the highway and press a button on a camera that takes thousandes of images per second and shoot straight ahead without changing the focus of your shot (constant shot). You then take all of the 100,000 photos snapped in a matter of seconds and lay them side by side, overlapping the redundant portions to create a solid "panoramic-style" image.
You have taken a picture of the same spot over and over again - only the cars have changed position, but when you put it together - it appears as one fluid image and relative positioning is absolute.
For the record - the one looks a clear winner to me - but I trust fully well that the image was enlarged and the line was placed directly on the tip of the one's nose and the green can clearly be seen between the nose of the rail horse and the line.