Agreed. But it should matter to him, and it sure doesn't sound to me like it does.
He does sound somewhat detached on the phone, but he knows that being a wailing blubbering mess doesn't help the dispatcher figure out what should be done. First responders and others with similar jobs that deal with crises typically get the job done first and cry/scream/etc. about it later. It's what they're trained to do. As another poster with a LEO husband pointed out, they typically fall back on their training and their work-mode/demeanor during a crisis.
I keep thinking about my own husband, who is an officer. The tone of voice didn't strike me as odd one bit, but I do agree with nells, my husband would be applying pressure to the wound from the get go. A few years ago, we had to call 911 for our newborn who was only a couple of days old. I was a mess, but my husband on the other hand was calm as a cucumber and knew exactly what to do in regards to first aid until the ambulance arrived. It really does come with the training and the job - you have to remove yourself from the situations to a certain degree in order to stay sane. That's what I hear in his voice, along with a hint of embarrassment, shame. Towards the end of the call, you can hear his emotions start to float to the surface. MOO.