If this is fake, they did a hell of a job on it. The lighting on that Deer is EXACTLY what is on the other subjects in the photo.
Besides casting no shadowing, the animals hindquarters are a joke. the rear hoof is just a stump.
You aren't out in nature much, are you? The deer is standing in grass...which would come up over its hooves the way you see it in this photo. No shadow? Why would it have a shadow? Nothing in this photo, other than the man's arm and the deer's leg (shadow cast by dog) has a shadow.
I've lived in the country my whole life, and there is no reason to believe this didn't happen. Hell, I almost walked into a deer standing by my house one morning. I said "excuse me" to it, and it finally ran away.
The Deer may also live on a farm. It's not uncommon for deer to become social and almost domesticated. They are very curious and usually quite docile.