In all respect I don't think issuing a chargeback is the way to go here. This doesn't solve anything really, and in fact it could really hurt a business. Why issue a chargeback when a company offers a refund ?
Ok, so customer didn't get what they paid for. Company takes a hardline stance & refuses to work with customer beyond telling them to buy an air mattress with the refunded fees. Where else does the customer have to turn at this point? The chargeback.
The whole point of putting it on the table and giving a 1 week deadline is exactly that it will hurt the business. You know it and they know it. Now suddenly they're not the only one with bargaining power in the relationship, so they might actually offer a partial refund of the actual rental based on the difference between what was offered & what was received. Or they might stick to their guns & fight the chargeback if they think they were correct in their initial assessment.
The chargeback is really like a turbo button - it boosts you up real quick past the grunt level CS people to actual decision makers who can and will do what they can to avoid the chargeback and maintain a positive relationship with you.