having a credit card and not using it does nothing to increase your credit score. Credit history is something they use to determine score, often times bigger loans are disapproved for having insufficient credit history, I have seen this many times in the Auto business. We will have to agree to disagree on this. Also having high available credit can be detrimental to receiving an additional loan, and credit scores are typically figured on debt to income ratio, not how much credit you have available on one card. Keep in mind this is someone just starting to establish credit, not someone with 10 cards a house and a history of paying off vehicles.
I do agree with your statement that carrying a balance does not show your ability to pay off over time, but making monthly payments over the course of a year does, and you can not do that with a 0 balance.