We may just have different viewpoints on this.
When I'm dealing with a deceased individual, I view my role as being their last guardian. There are exceptions. If he was breaking into a house and got shot, not so much. In an accidental death in which no one else was involved, and there was no criminal intent to harm another person, yeah, I view that as being private, and as the emergency responder, I would not share embarrassing information about the incident.
It behooves law enforcement to explain to the public what this person was doing besides driving responsibly and that it probably caused his death. If they can release information to the public about a drunk driver fatally smashing her vehicle into a tree then they can share the information in a case like this.