That's not quite correct for Hartzell's. From the
Hartzell Propeller Owner's Manual, page 6-9 & 6-10:
CAUTION 1: OVER-LUBRICATING AN ALUMINUM HUB PROPELLER MAY CAUSE THE GREASE TO ENTER THE HUB CAVITY, LEADING TO EXCESSIVE VIBRATION AND/OR SLUGGISH OPERATION. THE PROPELLER MUST THEN BE DISASSEMBLED TO REMOVE THIS GREASE.
...
CAUTION 4: DO NOT ATTEMPT TO PUMP MORE THAN 1 FL. OZ. (30 ML) OF GREASE INTO THE LUBRICATION FITTING. USING MORE THAN 1 FL. OZ. (30 ML) OF GREASE COULD RESULT IN OVER SERVICING OF THE PROPELLER.
(8) Pump a maximum of 1 fl. oz. (30 ml) grease into the lubrication fitting, or until grease emerges from the hole where the lubrication fitting or lubrication hole plug was removed, whichever occurs first.
NOTE: 1 fl. oz. (30 ml) is approximately 6 pumps with a hand-operated grease gun.
(a) For all tractor or pusher propellers with clockwise (standard) rotation when viewed from BEHIND the aircraft, apply grease to the lubrication fitting that is in the ENGINE-SIDE hub half.
(b) For all tractor or pusher propellers with counter- clockwise (backward) rotation when viewed from BEHIND the aircraft, apply grease to the lubrication fitting that is in the CYLINDER-SIDE hub half.