Observations of the upper chromosphere shows an enormous amount of intricate fine structure. Much of this comes in the form of linear features which are most often assumed to be well aligned with the direction of the magnetic field in the low plasma beta regime thought to dominate the upper chromosphere... We use advanced radiative MHD simulations including the effects of ion-neutral interactions (using the generalized Ohm's law) in the partially ionized chromosphere to show that the magnetic field is often not well aligned with chromospheric features. This occurs where the ambipolar diffusion is large, i.e., ions and neutral populations decouple as the ion-neutral collision frequency drops allowing the field to slip through the neutral population, currents perpendicular to the field are strong, and thermodynamic timescales are longer than or similar to the those of ambipolar diffusion. We find this often happens in dynamic spicule or fibril-like features at the top of the chromosphere. This has important consequences for field extrapolation methods which increasingly use such upper chromospheric features to help constrain the chromospheric magnetic field: our results invalidate the underlying assumption that these features are aligned with the field. In addition, our results cast doubt on results from 1D hydrodynamic models, which assume that plasma remains on the same field lines. Finally, our simulations show that ambipolar diffusion significantly alters the amount of free energy available in the coronal part of our simulated volume, which is likely to have consequences for studies of flare initiation. (read more)