Desensitized doesn't necessarily mean somebody doesn't have reactions to something. It just means they can compartmentalize those reactions and move forward and deal with the ramifications later.

EMTs, ER Doctors, and Nurses are largely desensitized to graphic trauma and can press through and get the job done. But that doesn't mean that they don't process those scenes later in both healthy and unhealthy ways (there's a few study out there that show ER staff have higher rates of alcoholism and substance abuse rates than the general public).

Tramua is trauma, whether you're desensitized or not.