That is not what the diode is helping against.
BLDC fans have internal half-bridge driver for each phase (typically 2 or 3 phases), these switches have implicit or explicit diodes for freewheeling the current stored in the winding inductance.
Just a simple MOSFET, either on the ground or Vcc side, is often used to PWM these fans. I do have a habit of adding a freewheeling diode though but the purpose is to freewheel the (fairly small) amount of energy stored in the parasitic indutance of the wiring. It may indeed be completely unnecessary. I would suggest probing for any voltage peaks between the fan output pin and ground with an oscilloscope.