Does the minimum level have some more complex effect in calculating the fan speed?
I did some experiments with oscilloscope, fan and a power supply with variable voltage.
Fan usually reports its speed using pulse width modulation. In the fan assembly there is a device called Hall effect sensor. It works by detecting magnetic field change as the fan rotates and it creates a number of pulses for each revolution of the fan. When the fan is operating very slowly or when the input voltage is very low, it may provide signal which is so deformed that the fan control circuitry could have serious problems getting any useful information form it. It could be that there is a software setting which would prevent fan from working so slow as to provide uninterpretable speed output.
Another point is fan starting voltage. Fan needs a certain voltage to start rotating. That voltage is lower than minimum voltage needed for the fan to rotate. It could be that software is designed in such way that it will not set fan's voltage below starting voltage for safety reasons.
Just to note: This is general information for computer fans and fan system in your computer may work a bit differently.