This is an ironic statement because the main character has been spending the middle part of the story being overjoyed that she will now be able to live the rest of her life freely now that her husband is supposedly dead. However, she died soon after. So she did spend the rest of her life being happy, but she was so happy that she died.
By having the doctor say that rather than Josephine or Richards, the discovery is given in an unemotional way. This allows for there to be no more introduction of the characters who knew her, and made sure that it was revealed unemotionally.