"low or no" charging rate is the key point in that troubleshooting bit - "low" means below the normal rate set on the regulator, which takes into account the max rate of charge that doesn't boil away the water in the battery .... you can't recharge a low battery real quick
if you have a normally operating system and you do something [leave the lights on] to really run the battery down, when the engine starts the ammeter will swing hard to charge [usually not all the way, but over half], but immediately, or quickly, it'll jump lower, and stay there for awhile before slowly starting to move back to neutral ... the regulator has sensed how low the battery is [feedback] and is controlling the rate of charge
Bill