That's valuable context. Most people don't have that relaxed a view about death, especially when it comes to people they care about. How long has it been since the last incident? If it's only been a month or two, then this is still very fresh for her. She probably needs more time in that case.

Is this the first time someone she cared about had a brush with death? She could still be in a bit of emotional shock from it. You may not be focused on it, but she still is. You've got a stark reminder of your mortality stenciled on your chest. That's something that will take some time to get past. While she is getting past it, don't push too hard or she'll just close up more.

In short, you have to be able to get into her head and see things the way she does in order to know what the next steps are. It sounds like she needs assurance, so your advised course of action is to find out how to provide that. That's going to be a lot harder as she is unwilling to talk about it. How are your soft skills? Can you get her to expound on what she is worried about? Does she have any close friends or family that she confides to? (not suggesting you pump them for information, just wondering about her emotional support structure).

Don't start taking the blame for it. It's a problem for both of you, as neither of you are happy as things are. At the same time, it's not anyone's fault either. The two of you just have different coping processes, and they aren't compatible in this case.