I guess a lot of this comes down to saying the right stuff and keeping your composure. Also, people can usually figure out when someone actually cares and is invested in fixing their problem. You don't have to shed tears to demonstrate this. Although, in some cases, the tears may actually come after the shift is over.
I can give you a little insight into this question, as most can guess, I have been a paramedic for a while, both pre-hospital and now in hospital. When I am with a patient, they get my full undivided attention, when they are telling me their history, I am actively listening and responding with questions as necessary to gain insight into the problem. I am empathetic, understanding, and compassionate, I am their shoulder to lean on. At the same time, I am formulating a working clinical impression, and what I need to do as a clinician. Its a balancing act, sometimes there are going to be patients that strike a nerve, especially when dealing with kids, even more specifically kids that have been abused. It takes everything I have to remain neutral and understanding when all I want to do is leave and have alone time. I have absolutely had times where it was too much, this is where CISD and having a peer counselor to talk to is important. Especially when you have to tell a family that despite everything you did, you couldn't save a family member. Some of this stuff will stick with you the rest of your life. The thing to remember through the whole thing though, we are their knight, the person with the answers, and it takes time to develop the ability to remain composed and professional in the face of massive emotional stress. But in order to be that person they feel like they can turn to, you have to learn how to be emotionally invested to an extent, but still remain unbiased and neutral when proper and necessary.
With that long winded response in mind, taking the middle ground for the right reasons is not a wrong response.Be emotionally accepting and compassionate, but remain professional enough to be able to operate as a clinician. It takes time to develop that balance, but is so very important in order to be the best you can.