We measured with unprecedented precision the induced polarization P(y) in (4)He(e,e'p)(3)H at Q(2)=0.8 and 1.3 (GeV/c)(2). The induced polarization is indicative of reaction-mechanism effects beyond the impulse approximation. Our results are in agreement with a relativistic distorted-wave impulse approximation calculation but are overestimated by a calculation with strong charge-exchange effects. Our data are used to constrain the strength of the spin-independent charge-exchange term in the latter calculation.