  In the past, spectropolarimetric data from Hinode/SP has been employed to
infer the distribution of the magnetic field vector in the quiet Sun. While
some authors have found predominantly horizontal magnetic fields, others favor
an isotropic distribution. In this paper, we investigate whether it is actually
possible to accurately retrieve the magnetic field vector in regions with very
low polarization signals (e.g: internetwork), employing the \ion{Fe}{I} line
pair at 6300 {\AA}. We first perform inversions of the Stokes vector observed
with Hinode/SP in the quiet Sun at disk center in order to confirm the
distributions retrieved by other authors. We then carry out several Monte-Carlo
simulations with synthetic data where we show that the observed distribution of
the magnetic field vector can be explained in terms of purely vertical
($\gamma=0\deg$) and weak fields ($\bar{B}<20$ G), that are misinterpreted by
the analysis technique (Stokes inversion code) as being horizontal ($\gamma
\approx 90\deg$) and stronger ($\bar{B} \approx 100$ G), due to the effect of
the photon noise. This casts doubts as to whether previous results, presenting
the distributions for the magnetic field vector peaking at $\gamma=90\deg$ and
$\bar{B}=100$ G, are actually correct. We propose that an accurate
determination of the magnetic field vector can be achieved by decreasing the
photon noise to a point where most of the observed profiles posses Stokes $Q$
or $U$ profiles that are above the noise level. Unfortunately, for noise levels
as low as $2.8\times 10^{-4}$ only 30% of the observed region with Hinode/SP
have strong enough $Q$ or $U$ signals, implying that the magnetic field vector
remains unknown in the rest of the internetwork.
