Eric, my very first electrical engineering job fresh out of Purdue in the late sixties was with Century Electric Motor Company, so I will try my best to "educate" you as you asked.
1) The purpose of a fuze orrrrrrrrrrrrr circuit breaker is to protect the branch circuit feeder wires from short circuit protection and overload. If you have a branch circuit that requires wire rated for 30 amps, then you use a 30 amp fuze or circuit breaker to PROTECT THE BRANCH CIRCUIT FEED WIRES...
2) Next if you use a motor you also want it protected against over current and overheat so to protect the MOTOR you use some sort of a thermal overload device which may be a device called a "thermal" or a "heater" in a starter or perhaps an internal thermal overload (red button you depress to reset)
3) The fuze or circuit breaker is to protect the BRANCH CIRCUIT FEED WIRES,,,,,,,,,The purpose of a thermal overload or heaters or thermals is to protect the MOTOR.
Perhaps what you heard refers to the engineering design fact that the branch circuit may be protected by EITHER a fuze or circuit breaker while the motor itself is protected by a device such as a heater or thermal which can melt open a link (if excess current) to protect the MOTOR i.e. you need BOTH branch circuit protection PLUS motor protection which is often a heater or thermal similar to a fuze in that a link actually melts and opens the circuit to prevent motor damage from excess current.
YOU NEED BOTH,,,,,,,BREAKER OR FUZE TO PROTECT THE BRANCH CIRCUIT FEED WIRES PLUSSSSSSS A THERMAL OVERLOAD DEVICE (heater or thermal acts like a fuze) TO PROTECT THE MOTOR
John T BSEE, JD