You misunderstood your role
You thought that your role was to fix the problem or label it unfixable.
Your actual role is to make the customer feel that they have been heard. You would have done that if you made it clear why their network was critical, and spent 5 minutes listening to how frustrated they are that they can't get anything done.
You wouldn't have solved any technical problem, but you would have solved your social one.
Cheers,
Ben
