Don't talk to the media if it's none of the public's business. Don't open a memorial fund if it's none of the public's business. Don't have a candlelight vigil with 1000 people. Don't have LE giving daily press conferences. Don't have LE allowing the media to come to a daily question and answer session. Don't interrupt regularly scheduled programming to give a press conference with no new developments. Don't make a case into a national story if you don't want people across the country asking questions.
As far as I could tell, the victim's family has said very little. Often times the public will show a humbling display of compassion and ask "can we help? what can we do". If the public wants to help or share in your mourning, do you REALLY consider that an open invitation to ask nosy questions like "where do you work" or "how big is your house"?
As for the rest of your statements -- I'm stunned. Are you suggesting that LE shouldn't do it's job? Sometimes LE must engage the press (because of an overwhelming interest in the case -- or to actively put information out in to the public domain and request assistance). Are you suggesting that if LE engages the media at all that it opens the victim and family up to what could lead to a public witch hunt?