If they weren't refusing refunds, I don't think people would be threatening chargebacks.
I've a mixed view on chargebacks for this - I fully agree that, if they get hit with a chargeback, a company is within its rights to stop any further service to that customer. So banning access to the customer's Origin account seems justified. But then there's the big question of why should a customer NEED "further service" for games they bought several years ago? So it all becomes wrong again.
I would agree with you if only 1 game was handled through Origin. Since ALL the games you buy from EA are linked to your account, that means that you can't play those games. So, the question remains : do I buy a game or do I rent a game ?
More, there is only one service / game, that is defective. Everything else is fine. So, they should be deprived of every services and games provided by Origin just because 1 game is faulty. I can not agree with that (or they refund everything up to the last coin).