That is corrrect, Once an office has any other reason to stop you, IE: your public drunk, seen ruuning from a crime. someone calls the cops cause you and your wife are in a loud disagreement in the street, etc, Then that office can and may demand you GWCL. The just of the law is you can't be stopped or detained for the sole purpose of investigating if you have a valid GWCL, once you have been stopped for any other reason you must produce your GWCL if ask or face arrest.
As a side note a GWCL is not required to carry in an automobile on your person or anywhere inside said automobile. However once you exit the automobile a GWCL is required. I bring this up BC some officers like to have citzens get out of their vehicles during traffic stops and wait at the rear of the vehicle. If you are armed on your person in your vehicle and do not have a GWCL and are ask by an office to step out of the vehicle this would be a good time to inform said office you are carring on you person and seek the officers direction on how you should proceed.