We present a precise measurement of double-polarization asymmetries in the (3)(He) over right arrow((e) over right arrow ,e'd) reaction. This particular process is a uniquely sensitive probe of hadron dynamics in He-3 and the structure of the underlying electromagnetic currents. The measurements have been performed in and around quasielastic kinematics at Q(2) = 0.25(GeV/c)(2) for missing momenta up to 270 MeV/c. The asymmetries are in fair agreement with the state-of-the-art calculations in terms of their functional dependencies on p(m) and omega, but are systematically offset. Beyond the region of the quasielastic peak, the discrepancies become even more pronounced. Thus, our measurements have been able to reveal deficiencies in the most sophisticated calculations of the three-body nuclear system, and indicate that further refinement in the treatment of their two-and/or three-body dynamics is required.