In the immediate period following someone’s death, is it too much to ask not to engage in or support rumor-mongering around the cause, for the sake of the famil

In the immediate period following someone’s death, is it too much to ask not to engage in or support rumor-mongering around the cause, for the sake of the family who is likely under tremendous stress and should not have to deal with the added stress of seeing such rumors? It hurts no one to wait some months to reveal details of a person’s death; at that time, outsiders can contemplate that info. Have some empathy.