I'm skeptical that this was a true diabolical possession. The Roman Ritual lists three signs of demonic possession, which are: 1) knowledge of secret distant or hidden things; 2) ability to speak many words in an unknown foreign language, and 3) the ability to do things that are physically impossible.
It is not clear at all that Anneliese Michel had any of these. Also, she had a long, severe history of mental illness, and this could easily account for her strange behavior. Unfortunately, she had the misfortune to suffer these symptoms after Vatican 2, when access to true Catholic priests was unavailable, who might have given an accurate diagnosis of her condition. As it was, she was left to the poor judgment of modernist clergy, who gravely mishandled her case, and their incompetence in identifying true diabolical possession may well have contributed to her death.
Really a sad case. I think if she had lived before Vatican 2 she would have been given the proper counsel and treatment.