It’s not based on ‘absolutely nothing’. The flight profile is arguably a good enough reason to make the suggestion, but the captain’s family’s own statement to the media is unequivocally a good enough reason to make it. And also to render your concern for their privacy and the mental well-being of the passengers’ families somewhat irrelevant at this point.
As for the ‘rule of two’... would a FO be concerned about an instruction from the captain to leave the flight deck shortly after seatbelts off? Or might the whole subject of pilot suicide be so taboo that they would think nothing of it?