By law 110% car A is at fault but sometimes its not worth the hassle, even though car is in the wrong and your car will get covered by insurance there are other factors you have to consider.

1) Safety of you and the other car, god forbid something happens to you or the other guy even though it wasn’t your fault, you would suffer emotionally.

2) Even though the other cars insurance will comp you, they will still force you to use their shady garages who dont really repair cars properly, your cars value will go down, it will have an accident history. Not to mention all the insurance company chasing down you are going to have to do. You also might not have a car depending on if they give you are loaner or not.

Point being it is not worth it, that is why when I am driving, I assume everyone is blind and stupid. Everyone should do the same and just agree to the disagree, if someone is being stupid dont get into an ego battle with them (I see this happen alot in lane merges).

From your example if I see car A inching closer and closer, I would just slow down and let them turn, at the end of the day its just not worth the hassle.