The Dzyaloshinskii-Moriya interaction (DMI) is believed to be operative in low-symmetry crystal structures lacking space-inversion symmetry. However, already in 1963, Arrott pointed out that even in a high-symmetry lattice, where the DMI would normally vanish, this interaction is present in the vicinity of any lattice defect. Based on these considerations and recent theoretical work, first experimental studies of the impact of the DMI on the spin-polarized magnetic small-angle neutron scattering (SANS) of polycrystalline magnets exhibiting a large density of microstructural defects have been performed. They demonstrated that an asymmetry in the difference between the two polarized SANS cross sections is induced by the DMI in nanocrystalline terbium and holmium as well as in mechanically-deformed microcrystalline cobalt. Here, we present a more complicated case, the nanocrystalline magnetically-textured soft magnet Vitroperm (Fe73Si16B7Nb3Cu1), where the interface between the FeSi nanoparticles and the amorphous magnetic matrix serves as the defect. The SANS cross section exhibits the polarization-dependent asymmetric term originating from the DMI. The effect has a magnetic field dependence and is less pronounced at higher fields until it eventually vanishes at full saturation. The result supports the generic relevance of the DMI for the magnetic structure of defect-rich ferromagnets. Furthermore, it shows that polarized SANS is a particularly powerful tool for investigating defect-induced DMI, which is a consequence of the unique dependence of the SANS cross section on the chiral interactions.