The Project of AI is a world-building endeavor, wherein those who fund and develop AI systems both operate through and seek to sustain networks of power and wealth. As they expand their access to resources and configure our sociotechnical conditions, they benefit from the ways in which a suite of decoys animate scholars, critics, policymakers, journalists, and the public into co-constructing industry-empowering AI futures. Regardless of who constructs or nurtures them, these decoys often create the illusion of accountability while both masking the emerging political economies that the Project of AI has set into motion, and also contributing to the network-making power that is at the heart of the Project's extraction and exploitation. Drawing on literature at the intersection of communication, science and technology studies, and economic sociology, we examine how the Project of AI is constructed. We then explore five decoys that seemingly critique - but in actuality co-constitute - AI's emergent power relations and material political economy. We argue that advancing meaningful fairness or accountability in AI requires: 1) recognizing when and how decoys serve as a distraction, and 2) grappling directly with the material political economy of the Project of AI. Doing so will enable us to attend to the networks of power that make 'AI' possible, spurring new visions for how to realize a more just technologically entangled world.