The polarization observed in the spectral lines of the He I 10830 Å multiplet carries valuable information on the dynamical and magnetic properties of plasma structures in the solar chromosphere and corona. Therefore, it is crucial to have a good physical understanding of its sensitivity to the various competing physical mechanisms. Here we focus on investigating the influence of atomic-level polarization on the emergent Stokes profiles for a broad range of magnetic field strengths, in both 90° and forward-scattering geometry. We show that, contrary to a widespread belief, the selective emission and absorption processes caused by the presence of atomic-level polarization may have an important influence on the emergent linear polarization, even for magnetic field strengths as large as 1000 G. Consequently, the modeling of the Stokes Q- and U-profiles should not be done by taking into account only the contribution of the transverse Zeeman effect within the framework of the Paschen-Back effect theory, unless the magnetic field intensity of the observed plasma structure is sensibly larger than 1000 G. We also point out that in low-lying optically thick plasma structures, such as those of active region filaments, the (horizontal) radiation field generated by the structure itself may substantially reduce the positive contribution to the anisotropy factor caused by the (vertical) radiation field coming from the underlying solar photosphere, so that the amount of atomic-level polarization may turn out to be negligible. Only under such circumstances can the emergent linear polarization of the He I 10830 Å multiplet in such structures of the solar atmospheric plasma be dominated by the contribution caused by the transverse Zeeman effect.