When generative AI (genAI) systems are used in high-stakes decision-making, its recommended role is to aid, rather than replace, human decision-making. However, there is little empirical exploration of how professionals making high-stakes decisions, such as those related to employment, perceive their agency and level of control when working with genAI systems. Through interviews with 22 recruiting professionals, we investigate how genAI subtly influences control over everyday workflows and even individual hiring decisions. Our findings highlight a pressing conflict: while recruiters believe they have final authority across the recruiting pipeline, genAI has become an invisible architect that shapes the foundational building blocks of information used for evaluation, from defining a job to determining good interview performances. The decision of whether or not to adopt was also often outside recruiters' control, with many feeling compelled to adopt genAI due to calls to integrate AI from higher-ups in their business, to combat applicant use of AI, and the individual need to boost productivity. Despite a seemingly seismic shift in how recruiting happens, participants only reported marginal efficiency gains. Such gains came at the high cost of recruiter deskilling, a trend that jeopardizes the meaningful oversight of decision-making. We conclude by discussing the implications of such findings for responsible and perceptible genAI use in hiring contexts.