Analysis of the Hanle effect in solar molecular lines allows us to obtain empirical information on hidden, mixed-polarity magnetic fields at subresolution scales in the (granular) upflowing regions of the `quiet' solar photosphere. Here we report that collisions seem to be very efficient in depolarizing the rotational levels of MgH lines. This has the interesting consequence that in the upflowing regions of the quiet solar photosphere the strength of the hidden magnetic field cannot be sensibly larger than 10 G, assuming the simplest case of a single valued microturbulent field that fills the entire upflowing photospheric volume. Alternatively, an equally good theoretical fit to the observed scattering polarization amplitudes can be achieved by assuming that the rate of depolarizing collisions is an order of magnitude smaller than in the previous collisionally dominated case, but then the required strength of the hidden field in the upflowing regions turns out to be unrealistically high. These constraints reinforce our previously obtained conclusion that there is a vast amount of hidden magnetic energy and unsigned magnetic flux localized in the (intergranular) downflowing regions of the quiet solar photosphere. This work has been presented by tet{a4 AT05}.