As high-speed, agile robots become more commonplace, these robots will have the potential to better aid and collaborate with humans. However, due to the increased agility and functionality of these robots, close collaboration with humans can create safety concerns that alter team dynamics and degrade task performance. In this work, we aim to enable the deployment of safe and trustworthy agile robots that operate in proximity with humans. We do so by 1) Proposing a novel human-robot doubles table tennis scenario to serve as a testbed for studying agile, proximate human-robot collaboration and 2) Conducting a user-study to understand how attributes of the robot (e.g., robot competency or capacity to communicate) impact team dynamics, perceived safety, and perceived trust, and how these latent factors affect human-robot collaboration (HRC) performance. We find that robot competency significantly increases perceived trust ($p<.001$), extending skill-to-trust assessments in prior studies to agile, proximate HRC. Furthermore, interestingly, we find that when the robot vocalizes its intention to perform a task, it results in a significant decrease in team performance ($p=.037$) and perceived safety of the system ($p=.009$).