We report on a precise measurement of double-polarization asymmetries in electron-induced breakup of 3He proceeding to pd and ppn final states, performed in quasi-elastic kinematics at Q 2 = 0.25 (GeV/c)2 for missing momenta up to 250 MeV/c. These observables represent highly sensitive tools to investigate the electromagnetic and spin structure of 3He and the relative importance of two- and three-body effects involved in the breakup reaction dynamics. The measured asymmetries cannot be satisfactorily reproduced by state-of-the-art calculations of 3He unless their three-body segment is adjusted, indicating that the spin-dependent part of the nuclear interaction governing the three-body breakup process is much smaller than previously thought.