An undisclosed change in ownership – does it need to be official/legal to nullify an auto insurance policy?

Person A legally owns a Lexus and has it insured.

Person B is a friend of Person A.
Person B legally owns a Prius and has it insured.

They switch cars.
They both understand between each other that the Lexus now belongs to Person B and the Prius now belongs to Person A, but they don’t do a title change or bill of sale.

Person B gets into a collision with the Lexus and is at fault because the other car was parked and unoccupied in their own driveway at the time.

The other party files a claim with the insurance policy which Person A previously paid for to cover to Lexus, which is still active.

Will the insurance deny liability because there was an undisclosed change in ownership? Or will they still accept liability, since the undisclosed change in ownership wasn’t done legally/officially?

I understand that the answer may depend on the specific insurance company and policy. I’m asking because I don’t know if the answer would actually be common across all insurance companies and policies. Thank you!