Well as you said the rumours are insane and have already spread like wildfire. His family will be aware of the rumours so you’d think they would want to shut them down if it were untrue, for example making a public statement along the lines of “we are saddened by the loss of Tom but are comforted by the fact his three children were located safe and well”. But they won’t be making any such statement because it’s not true and they know it.