Well, I agree that I would freak out if I saw a dead body unexpected in my closet. But this wasn’t her closet or her house, and she knew she was present at a crime scene, not there to socialize. Aside from that, I disagree with you that a doctor would only be used to a dead or injured body in a “controlled” environment. Even the doctors who end up practicing in a relatively “posh” specialty still have to do their training in a wide variety of medical disciplines, including trauma and emergency. Especially in a major metropolis like NYC, if you spend just one day treating patients in the ER you’ll see far, far worse than that dead body. There’s no “controlled environment” where you can become a doctor in the U.S. by having only patients brought to you that are clean and pristine. You have to handle accident victims, murder victims and people who have experienced terrible violence, in addition to illness. 

This all loops back around to the fact that they needlessly changed Joan’s background: if she was still a competent military surgeon (or, as in Watson & Holmes, an ER/trauma surgeon) rather than a disgraced civilian doctor, there would be no question that she wouldn’t get squeamish at the sight of a dead body. We would know that she’s a professional who’s see far worse. But the writers/producers of Elementary robbed the character of her medical and professional competence at the outset, then added in a scene where she was portrayed as “the squeamish girl” who needs to be (literally, look at the blocking of the scene) shielded by the male characters (one of whom is neither a cop nor a doctor and who should be far less experienced than she is). It’s just another symptom of how in the pilot they did everything to undermine us meeting the character as a strong, professional woman and did nothing to build her up. How in the world is she going to help Holmes solve cases when, instead of giving her medical opinion about a victim, she has to run out of the room?