Are solar chromospheric fibrils tracing the magnetic field?

Fibrils are thin elongated features visible in the solar chromosphere in and around magnetized regions. Because of their visual appearance, they have been traditionally considered a tracer of the magnetic field lines. For the first time, we challenge that notion, by comparing their orientation to that of the magnetic field, obtained via high-resolution spectropolarimetric observations of Ca ii lines. The short answer to the question posed in the title is that mostly yes, but not always.