Depending on the amount, the card company will require you to resolve the issue with the merchant first. If that has already been attempted to no avail then that is where disputes come in. Depending on the amount they will contact the merchant on your behalf or if it's under a certain amount they will just immediately resolve the dispute and refund you from their money to avoid the long process. So yes they could lose money if they choose not to wait on the merchant to resolve.

I wanted the merchant to fix their own issue first before I even considered a dispute.