In this paper, we analyze two key claims offered by recruitment AI companies in relation to the development and deployment of AI-powered HR tools: (1) recruitment AI can objectively assess candidates by removing gender and race from their systems, and (2) this removal of gender and race will make recruitment fairer, help customers attain their DEI goals, and lay the foundations for a truly meritocratic culture to thrive within an organization. We argue that these claims are misleading for four reasons: First, attempts to "strip" gender and race from AI systems often misunderstand what gender and race are, casting them as isolatable attributes rather than broader systems of power. Second, the attempted outsourcing of "diversity work" to AI-powered hiring tools may unintentionally entrench cultures of inequality and discrimination by failing to address the systemic problems within organizations. Third, AI hiring tools' supposedly neutral assessment of candidates' traits belie the power relationship between the observer and the observed. Specifically, the racialized history of character analysis and its associated processes of classification and categorization play into longer histories of taxonomical sorting and reflect the current demands and desires of the job market, even when not explicitly conducted along the lines of gender and race. Fourth, recruitment AI tools help produce the "ideal candidate" that they supposedly identify through by constructing associations between words and people's bodies. From these four conclusions outlined above, we offer three key recommendations to AI HR firms, their customers, and policy makers going forward.