This summary is not the rule. The rule text controls.
If a judge appoints a lawyer to take on a case, the lawyer generally has to accept it. Lawyers can't just turn down an appointment because they don't want the case or don't like the client. Courts rely on lawyers to step up and represent people who need it, even if the case isn't something the lawyer would have chosen on their own.
There are only a few good reasons a lawyer can refuse an appointment. First, if taking the case would force the lawyer to break ethics rules or other laws, they can say no. Second, if the case would create a financial hardship that's too much to handle, that's also a valid reason. Third, if the lawyer feels such strong personal dislike or conflict with the client or the case itself that it would hurt their ability to do a good job, they can decline.
Outside of these situations, lawyers are expected to accept appointments they're given. This rule exists so that people who need legal help, especially those who can't afford a lawyer, can still get proper representation in court.
