A displacement of the heliospheric current sheet (HCS) south of the helioequator by similar to 10 degrees was proposed by Simpson et al. (1996) as a possible explanation of the north-south asymmetry in the galactic cosmic rays observed by Ulysses during its first fast transit in 1994-1995. The idea was not supported by magnetic field measurements on Ulysses and, on this ground, was dismissed by Simpson et al. (1996). In addition, Erdos & Balogh (1998) argued that any north-south symmetry was unlikely as there should be flux balance between the magnetic sectors of opposite polarity. Nonetheless, many in the scientific community have accepted the original suggestion of Simpson et al. (1996) that a displacement of the HCS was responsible for the cosmic ray asymmetry. In this paper, using a magnetohydrodynamic model of the solar corona and solar wind that includes both dipole and quadrupole magnetic source terms, we show that a north-south asymmetry of the magnetic field on the Sun does not give rise to a displacement of the HCS. The lack of displacement of the HCS results from a latitudinal redistribution of magnetic flux near the Sun where the plasma beta << 1. The latitudinal redistribution is a direct consequence of the magnetic field gradient between pole and equator. Near the Sun, the latitudinal gradient in magnetic field generates meridional flows directed equatorward that tend to relax the gradient in the magnetic field (to make it more latitude-independent) as heliocentric distance increases. If there is an asymmetry between north and south magnetic field strength then the meridional flows are also asymmetric (i.e., stronger in the hemisphere of stronger magnetic field). Because the magnetic fluxes (positive and negative) in the hemispheres must be equal, the redistribution shifts the HCS in the direction of the hemisphere with a weaker field and brings the field strength on both sides of the HCS into balance by similar to 16 R-circle dot. At larger distances, where the magnetic field is relatively weak (beta >> 1), the HCS can be displaced if there is a difference in total pressure between the hemispheres.