I can. I have to remember not to smile when something bad happens. I smile for two reasons.
1. I feel such sympathy for anything that is hurt. It's like an overwhelming love and gentleness, I want to somehow make up for their pain by saying everything will be alright, life will be good now, I'll make everything perfect. It's the exact same feeling as giggling and laughing.Except the emotion is so intense.
2. Any problem is an opportunity. If I see an injured animal I get excited and almost joyful because here is a chance to make the world a much better place - I can't change the fact that animals get hurt, but I CAN fix it. That gets me excited. That cheetah could have been saved in exactly the same way that people are saved - we could have an ambulance service, support services, etc. Obviously to achieve this would require a complete revolution in how the entire world works - in order to make saving every sick animal economically viable, as it is for saving humans. I am under no illusions about the scale f the task, but scale is something we can plan for. People just lack ambition.
It is funny that NTs accuse aspies of lacking empathy, when they are the ones who happily ignore suffering animals. And it is funny that NTs accuse aspies of rigid thinking. It is, instead, focused thinking - not the same thing at all. I see NTs as very rigid. They see a sick animal, or other problems, and just accept it as unchangeable. I see ways to change everything. Every problem can be fixed. Of course, some problems require either hundreds of years (e.g. travel to other planets) or complete sacrifice of all other interests (e.g. solving global poverty) or a complete change in how we see the world (e.g. solving death), so everyone else says "it cannot be done." They say that because they psychologically cannot handle the implication, that they could have solved it but chose not to because the price was too high.
So yeah, I get excited by bad things because that is my purpose in life, to fix them.