No, the court can also say that two laws are inconsistent. In this case, there is a judicial ruling (Chevron) that has stood for a while, that they are saying

No, the court can also say that two laws are inconsistent. In this case, there is a judicial ruling (Chevron) that has stood for a while, that they are saying is inconsistent with a law (the APA). The constitution is not in this ruling at all. Generally, laws override judicial rulings unless the constitution is in question.