There is plenty of evidence to contradict TFA's claim, but like you point out I see no evidence premiums will or would drop. Insurance companies are about making money. If they can charge the rate, they will charge the rate. If you want to fix insurance, go back to Insurance companies being Non-Profit organizations.
You make it sound like insurance companies operate in a vacuum. If an autonomous car is safer and rates don't go down then someone new will come along and undercut the existing players. More importantly, if liability gets shifted to the car manufacturers then if rates are not what they consider reasonable then it's very possible for them to just self-insure their entire fleet and cut out the insurance companies completely.