There's a very broad statement on Delta's website:
We reserve the right to refuse any bag that has a size, weight or other condition that poses a safety or annoyance risk to other passengers and/or crew, or baggage that is unsuitable for transportation on the aircraft.
So if they are being stubborn about something, it would probably come down to how badly you want to make your flight vs. dealing with the consequences of trying to prove to them that they refused it unreasonably.