If it's a "self driving car" that the person "owns" - Yes.
If it's a "Taxi service" that the person is using - No.
If it's a car they own, they (should) have the ability to override the AI system and avoid the accident (ignoring nuances) - therefore owning responsibility.
If it's a Taxi they would be in a position where they can't interfere with the operation of the system - therefore the taxi company owns the responsibility.
Rightly or wrongly, this model of intervention capability is what that I'd use to answer these types of questions.
If it's a car they own, they (should) have the ability to override the AI system and avoid the accident (ignoring nuances) - therefore owning responsibility.
If it's a Taxi they would be in a position where they can't interfere with the operation of the system - therefore the taxi company owns the responsibility.
Rightly or wrongly, this model of intervention capability is what that I'd use to answer these types of questions.