Magnetic materials are not linear in the way they become magnetised - the plot of magnetic hysteresis shows this:
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/hyst.html
Because a pickup pole piece (which is not necessarily the magnet) is within the coil of a pickup it has an effect on the changing electromagnetic flux that induces the currents in the coil. We are talking about tiny effects here but I would expect that it is these effects that help define the tone of a pickup. Then there is the grade of copper used in the coil, the dielectric effect of the insulation used on the copper, the interaction of the guitar string itself (if electric currents weren't induced in the string then the pickup would not work), and last but not least the 'strength' of the magnet. Perhaps some of these effects are over-sold, but not all pickups are born equal. The nice linear equations in text books describe idealised electrical components operating in free space - the real world isn't that simple.