This is a very poor show from BA. Obviously once landed at EDI, the weather left the flight crew no choice as ABZ was unreachable.
If in the OP’s shoes starting at LAX I would have been exhausted and not fit to drive. I would probably also have been marginally inebriated after all that time! I certainly would not have hired a car. It’s up to the airline in this circumstance to provide duty of care. Just abandoning you to fend for yourselves is unacceptable. I suspect that some people would not have been able to manage the onward journey themselves and would have been very distressed.