Delta T of 15 to 20 degrees isn't an old wives tale, it's a well known design parameter of most residential type AC units used in Homes, RVs and Autos. It's not an indication of what the system is capable of but instead an airflow to Temperature relationships that results in maximum performance in the conditions the unit is designed to operate in. An HVAC mechanic will have access to technical data detailing the optimal temp changes to expect from the particular system being looked at, and take troubleshooting from there. Changes of more than 20 degrees in most systems and you start looking into the possibility of the unit being low on refrigerant, or clogged filters or other issues that might be reducing airflow. Temp changes that are to low could again be again low refrigerant, either through causing icing, or low enough to reduce cooling etc. etc.
As others have mentioned, your AC generally continually recycles the air within the home/rv and auto depending on setting. How effective it is at cooling that airspace is dependent on both temperature and volume of air processed. Designing the system to be the most efficient at doing that generally results in a system with an intake to output temperature differential across the cooling heat exchanger of approximately 20 degrees.