Yes, it "counts more" as in it creates a higher hurdle for the family to overcome, and it does this in two ways:
1. The family member gets to witness a family member in a situation that they can't process. Family members can process Grandpa dying in his sleep after a ripe old age. It's harder for family members to process Grandpa getting chopped up by a garden tiller on a 100hp tractor, especially with all the "visuals" that get burned into their minds. When a person sees some kind of incident, they often wonder "how that happened". When you try to remember grandpa dying in his sleep, it's easy. When you try to remember grandpa getting chopped to bits in a tiller as your last memory of him it damages it.
2. Family member or not, grotesque deaths, where a human being is turned into something that doesn't resemble a human being creates a mental barrier to be overcome. When a body made in God's image is destroyed in an unnatural way it creates a mental barrier.
In a death where Grandma dies in her old age in sleeping in bed most family members can accept that easily within the first hour. Other kinds of death, I.E Grandpa in the garden tiller, are not as easily accepted.
Anything with kids, or young parents, or a generally grotesque death are not as easily accepted.