For about a decade, spectropolarimetry of He I λ10830 has been applied to the magnetic diagnostics of the solar chromosphere. This resonance line is very versatile as it is visible both on disk and in off-limb structures, and it has a good sensitivity to both the weak-field Hanle effect and the strong-field Zeeman effect. Recent observations of an active-region filament showed that the linear polarization was dominated by the transverse Zeeman effect, with very little or no hint of scattering polarization. This is surprising, since the He I levels should be significantly polarized in a conventional scattering scenario. To explain the observed level of atomic depolarization by collisional or radiative processes, one must invoke plasma densities larger by several orders of magnitude than currently known values for prominences. We show that such depolarization can be explained quite naturally by the presence of an unresolved, highly entangled magnetic field, which averages to give the ordered field inferred from spectropolarimetric data, over the typical temporal and spatial scales of the observations. We present a modeling of the polarized He I λ10830 in this scenario, and discuss its implications for the magnetic diagnostics of prominences and spicules, and for the general study of unresolved magnetic field distributions in the solar atmosphere.