I believe the families involved definitely deserve privacy. The didn’t ask for the crime to happen (in most cases). I think they should be able to seek justice without being harassed by the media or the public. If they want to talk, it’s up to them, but they shouldn’t be forced to do so.
As for the rest of us knowing every single fact of the incident, no, I don’t think we (general public) have a “right” to know every single detail. (I’m talking about every little thing, not just the big details.) I think the jury needs to know the facts to make a fair decision, but I think that is different than the general public being told every little detail. I also don’t think all court proceedings should be open to the public just for the safety of the victims and witnesses. It is all very dependent on the case and the situation.