I would say that I was/am sympathetic, not empathetic. I recognize that it's a tragedy for them, but I don't feel similar emotions.
I'm curious if the reason behind such vocalization is because very few people actually feel empathy. A facade for their feelings of joy/relief that such things didn't occur to someone they know.
I, as you probably guessed, don't have any children. I presume my feelings on the subject would be different if that weren't the case.