The increasing use of generative AI for resume screening is predicated on the assumption that it offers an unbiased alternative to biased human decision-making. However, this belief fails to address a critical question: are these AI systems fundamentally competent at the evaluative tasks they are meant to perform? This study investigates the question of competence through a two-part audit of eight major AI platforms. Experiment 1 confirmed complex, contextual racial and gender biases, with some models penalizing candidates merely for the presence of demographic signals. Experiment 2, which evaluated core competence, provided a critical insight: some models that appeared unbiased were, in fact, incapable of performing a substantive evaluation, relying instead on superficial keyword matching. This paper introduces the "Illusion of Neutrality" to describe this phenomenon, where an apparent lack of bias is merely a symptom of a model's inability to make meaningful judgments. This study recommends that organizations and regulators adopt a dual-validation framework, auditing AI hiring tools for both demographic bias and demonstrable competence to ensure they are both equitable and effective.