A journalists job to share the news and make information available to the general public. That duty, not a responsibility to care about the feelings of a third party, is what news sources should attend to.
In the absence of accurate news reports the public will have to rely on rumors, which can be much worse than the truth.
News sources should always reveal exactly how a celebrity died. Celebrities are in the public eye and their life is broadcasted all over the world. They choose to share their life with the world and when they die they owe it to everyone to explain situations to them. Explaining exactly how a death happened will give closure to everyone
By not reporting these things the media allows rumours and conjecture to fly. This also happens when they are less than accurate look for the trailer of the documentary soaked in bleach it is about kurt Cobain and his supposed suicide. The media reported an absurd amount of inaccuracies. So yah it's pretty important that the news does there job right.
Privacy of the nature of death will be able to protect the members in his/her family. Speculation and rumours do not directly harm the members of family but by allowing news sources to know about the nature of the death, the family might be emotionally hurt. Furthermore, rumours would be more likely to spread.
When you choose a life in the spotlight, the public will always want to know the details, including and maybe even especially surrounding death. Fans and public interest are one of the main people become rich and famous. We follow celebrities lives, like characters in their movies. To have a celebrity death as tragic and unfortunate as it is, generates mass public interest. We need to know what happened to those we love, or even love to hate.
News reporters should not reveal all the specifics of how a celebrity dies, unless it forms a compelling part of the story. Common decency should govern the decision of how and when to disclose the specifics on how a celebrity dies. There is no reason to disclosed death details just for shock value.
As usual, I do not agree with the 'always' part of the question. To be honest, I don't think there is a moral, ethical, or otherwise important or binding imperative for the media to be obliged to report the causes of every celebrity death. The public has the right to know about things that are directly related to them, such as how the government's new department is going to run on trade funds, or how the factory in their neighbourhood is going to pollute the environment, but this isn't one of them these cases at all.
I think the media should use their discretion. If the family members request them not to, then by all means refuse to do so. Be a nice person and don't try to hurt their feelings. If they agree to it, then the media can as long as they do not add speculation or sensationalist elements that would attract eyeballs but be disrespectful to the deceased.