I think it also illustrates where this article goes wrong. You don't say NO to the client, you say NO to a potential customer before they become the client.
Citing the second part of the comic - Client: "Our last designer was an IDIOT". Then the next appropriate question is - What idiot hired/managed him?
Or just make sure you have an escape clause in your contract. Maybe the last designer actually was an idiot. I've found that if you behave like the doctor (in the article) it's often quite easy to steer the course of projects with even very difficult clients.
Citing the second part of the comic - Client: "Our last designer was an IDIOT". Then the next appropriate question is - What idiot hired/managed him?
You're about to become the 'last designer'