Look at it this way. If you went out and bought a 5,000 btu window air conditioner for your bedroom at home, you coud run it off a 15 amp circuit indefinitely. My daddy did this all while I was growing up and my mom runs the A/C in the same house to this day. When they buillt the house in 1953, 15 amp circuits were the standard of the industry.
You answered your own question. If the appliance runs on a 15 amp circuit in your house, it will run on a 15 amp circuit in your camper. The only way to settle this is to make up a short "extension" cord of separate conductors then put a clamp on amp meter on the hot leg while running the A/C on a 15 amp circuit. Take a picture of the amp meter display and post it.
2006 23B Hybrid with 10k round bar WDH
2011 F150 4x4 SCREW Ecoboost, Max Tow, Integrated TBC, 3.73 LS axle, Firestone Ride Rite airbags.