Yes that is true, if you have a high enough relationship with your pet, BFF, they often will attempt to plead with the Grim Reaper to spare your life.
Unlucky and Loser traits also prevent accidental deaths, but not death by old age, because the Grim Reaper thinks you're suffering life is amusement to him and others.
I had one time where I had a fire, the Sim died, he had a death flower, after my Sim gave it to him, another fire started on the lot and instead of whisking away, the Grim Reaper ran over and put the fire out.
He seems to like toddlers a lot. On more than one occasion when a Sim dies, after he takes the Sim, I've had him play with the kid. It was really cute when he picked up the teddy bear and did the "Talk through" interaction.
I got the serenity retreat and it comes with a massage table and I was able to give the Grim Reaper acupuncture.