The stapler uses a small opto sensor, normally triggered by the paper being inserted and blocking the sensor, to fire off an interposing SCR that powers the plunger solenoid. SCRs can be self-commutated (turned on without a trigger) if there is a rapid change in voltage on the line, called dv/dt (delta voltage / delta time), otherwise known as a "spike". Switching the motor on or changing speeds produces enough of a dv/dt spike to fire the SCR on the stapler. If they were plugged into different outlets, the added impedance of the wire would dampen the spike and not cause the stapler to self-fire. Tell her to move the fan or stapler, or just live with it, it isn't a real problem, just a curiosity. If she insists, take apart the stapler and put in a little RC snubber on the line coming in, about 1kohm and 1mf should do it. The snubber will get warm though.
