Simon, I am not a doctor, though I have taken quite a few psychology classes and I have done volunteer work with battered women. I am not certain about what type of mental illness(es) Anna suffered from, but it is clear to me that she was mentally ill. Her behavior throughout her life suggests to me that PTSD might have been something she suffered from. I also suspect that she suffered from bipolar disorder, caused by the blow to her head, which might explain her mood swings and erratic behavior. I don't know enough about bipolar disorder to say that she met all the criteria for it, but the mood swings certainly suggest that it was a possibility.
It is a shame that so many of the people who knew Anna best, and who lived with her, are not alive now to be interviewed by a psychiatrist, who might be able to make an accurate diagnosis based on their testimony as well as the incidents recorded in Kurth's book.
It is true that different people react in different ways to traumatic situations; some people are scarred for life, while others seem unaffected.
For example: Charles II was hunted throughout England (forced to hide in a tree at one point) after a failed attempt to regain his father's throne. A price was put on his head and he heard soldiers threatening his life. He spent ten years wandering the Continent in poverty and in fear of assassination attempts. His young sister Elizabeth died in captivity in England; many believed that she was poisoned.
After his Restoration, Charles happily returned to the palace of Whitehall in London, where he lived for most of his reign. His father had been beheaded on a scaffold erected just outside the Banqueting Hall of Whitehall. Charles used the Banqueting Hall without any undue comment, and was friendly to all of his people, even those who had fought against his father during the Civil War. He was merciless only to regicides. He even permitted the sons of Oliver Cromwell to return to England and live on their estates in peace.
Marie-Therese returned to France after Napoleon's fall, but unlike the Merry Monarch, she made it clear that she could not forget the past. Marie-Therese had a tendency to shut herself in her rooms to weep; unlike Charles, she was not hail-fellow-well-met. When she left the palace, her carriage took circuitous routes throughout Paris because she refused to drive near squares where guillotines had been set up; she did not wish to see the sites where her parents and aunt had died. She paid a single visit to the site where the Temple prison had stood, and paid to have a church erected on the property. She also tried to avoid other landmarks.
Marie-Therese was clearly frightened by the crowds in Paris, and could not bring herself to smile or wave to them. She spent a great deal of her time praying, and treasured the bloody shirt that her father had worn on the scaffold as well as other relics of her lost family. Marie-Therese could not forgive and forget; she quickly became very unpopular. She was less than friendly to the new nobility created by Napoleon. She grimly soldiered on through her life, but she was never a happy woman. She was also tormented by men who came forward claiming to be her brother Louis XVII.
It must be added that neither Charles II nor Marie-Therese were physically assaulted in a traumatic event that left them brain-damaged. Whoever she was, Anna did survive such a traumatic event.
As for the Titanic survivors, I seem to remember reading that one survivor said that he could never attend a baseball game, since the roar of the crowd at the stadium reminded him of the screams of the people who were left to drown or freeze to death after the Titanic sank.
Everyone has different ways of coping with tragedy. I think Anna's coping skills were impaired by brain damage and mental illness.
All of this is just my opinion and your mileage may vary.
