The first time any of my Sims ever experienced this (somewhat) was last night. Except, my Sim didn't even get a call or a notification at all, she just suddenly got the sad moodlet. I had to go look in her relationships to see who died. It was a co-worker she'd only known for a few days with limited interaction. His ghost was listed in her relationships still as a co-worker, but the next time she went to work, he was replaced with another townie. He's not in households management either.
What really bums me out is this guy had won the lottery and I was contemplating having my Sim marry him for his money and then send him to 'the deep forest' herself with one last woohoo. I know that sounds, well, cold. But hey, that's a much happier way to go for a millionaire than just dying alone of old age 'somewhere.' I don't even know where to find his urn if it even exists since he was 'not in world.' :/
Anyway, I think it would be better to only get notices for family and close friends with varying degrees of mourning depending on how strong the relationship happened to be with your Sim. I also agree that if the Sim was an enemy, you wouldn't necessarily get the sad moodlet, but perhaps happy, fine or none at all depending on how deeply the Sim was disliked and any prior relationship they may have had. I can see how that might get too complicated though so maybe that's why they just assigned a blanket 'sad' moodlet for everyone your Sim knew. I don't know...*shrugs*