In the face of rapidly advancing technologies, evidence of harms they can exacerbate, and insufficient policy to ensure accountability from tech companies, what are HCI opportunities for advancing policymaking of technology? In this paper, we explore challenges and opportunities for tech policymaking through a case study of app-based rideshare driving. We begin with background on rideshare platforms and how they operate. Next, we review literature on algorithmic management about how rideshare drivers actually experience platform features -- often to the detriment of their well-being -- and ways they respond. In light of this, researchers and advocates have called for increased worker protections, thus we turn to rideshare policy and regulation efforts in the U.S. Here, we differentiate the political strategies of platforms with those of drivers to illustrate the conflicting narratives policymakers face when trying to oversee gig work platforms. We reflect that past methods surfacing drivers' experiences may be insufficient for policymaker needs when developing oversight. To address this gap and our original inquiry -- what are HCI opportunities for advancing tech policymaking -- we briefly explore two paths forward for holding tech companies accountable in the rideshare context: (1) data transparency initiatives to enable collective auditing by workers and (2) legal frameworks for holding platforms accountable.