We present numerical experiments aimed at understanding why near-infrared observations systematically deliver weak magnetic fields in the internetwork, whereas analyses based on visible lines indicate that kG fields are ubiquitous. Synthetic noisy Stokes V profiles of the iron lines at 6302 Å and 1.565 mu m have been produced under varying conditions in an effort to simulate polarized spectra coming from the internetwork. An inversion technique has been applied to the profiles, as it is usually done with real observations, in order to derive the distribution of magnetic fields in the simulated region. Our results show that infrared lines yield distributions which are very similar to those used as input for the simulation, while visible lines are to a large extent affected by noise. Analyses based on the Fe I lines at 6302 Å may lead to an overabundance of kG fields if the signal-to-noise ratio in Stokes V is poorer than about 10. A particular example is shown where strong fields are retrieved in nearly 30% of the pixels of a simulated internetwork region in which only fields of 200 G exist.