This summary is not the rule. The rule text controls.
If a judge asks a lawyer to take on a case, the lawyer usually has to say yes. Lawyers can't just turn down an appointment because they don't feel like taking the case or because the client seems difficult. Courts count on lawyers to step up and represent people who need help, even when it's not a case the lawyer would have picked on their own.
There are a few real reasons a lawyer can refuse. If taking the case would force the lawyer to break the law or violate ethics rules, they can say no. If the case would cost the lawyer too much money to handle properly, that's also a valid reason. And if the lawyer finds the client or the situation so disturbing that it would get in the way of doing a good job, they can ask to be excused too.
These exceptions exist so lawyers can raise real problems, not just personal preferences. A lawyer can't dodge an appointment simply because the case is unpopular, the client can't pay much, or the work seems unpleasant. The rule pushes lawyers to serve the court system and the public, while still protecting them from situations that would actually cause harm or an unfair burden.