You are quite correct. Here it is in black and white!
" Field current supply is provided from two different sources - from the alternator itself, via the diode trio, and from the battery, via the alternator warning lamp. When you first get in the car and turn the key on, the engine is not running and the alternator is not spinning. At this time, the voltage/current source for the field current is from the battery, through the ignition switch, and through the warning lamp. After the engine is started, and the alternator is up to speed, the output of the diode trio is fed back to the regulator, and serves as a source of current for the field current. At this time, the alternator is self sustaining, and the battery is no longer needed to power the electrical system"