I can't say for sure, but I don't see how a celebrity's child's passing would have any impact on me, even if they shared a condition. What if it was a car accident and I had lost a child to a car accident? Why would it matter?
So by that reasoning you must be in constant mourning for everyone who dies. Someone dies every minute. Are you in perpetual grief or does it make YOU feel better showing others that you "care"? I'm not trying to be an a-hole. You can look through past posts and find similar sentiments from me. I think people get some sort of satisfaction by expressing "remorse" for someone they've never met. It's a strange phenomenon. Certainly it's sad for the Travoltas but for any of us to actually be sad means either you don't care about non-famous people's deaths or you are essentially always sad about every death.