OK, that seals it then. Provided that your bag was 50 lbs or less, as you stated, AC is incorrect, and you should file a DOT complaint against them, not UA. AC's baggage fees are completely irrelevant. Under 14 CFR §399.87, "For passengers whose ultimate ticketed origin or destination is a U.S. point, U.S. and foreign carriers must apply the baggage allowances and fees that apply at the beginning of a passenger's itinerary throughout his or her entire itinerary." It is UA's fees, which are correctly detailed on your receipt, that apply, by law.