You can defuse many difficult situations by empathizing with the customer. The customer’s angry; you say, “This has got to be very difficult.” The customer’s upset; you ask, “This is frustrating, isn’t it?”
You remove the customer’s ability to argue.
When you say, “This has got to be very difficult,” she can’t say “No, it’s not!” Her only response is “Yes, it is.” And the two of you have something to agree about. Then you work together for a solution. You’ve bridged the gap.