Under the conditions you described, I think it can occur easily. Part of the problem is that the air conditioner is not only having to cool the air inside the motorhome, but everything else inside that is near 103F also. All the cabinets, beds, furniture, dishes, etc...
Whether it's 15,000 or 13,500 BTU/hr air conditioner (only 11% difference) these air conditioners don't have all that much excess capacity to start with when motorhome is parked outside on a hot sunny day, so it takes a long time for the initial cool down.
It helps to turn the AC on in the morning to keep the motorhome from getting so hot.
I'm in South Florida and yesterday was indeed hot. I went to visit a friend at 2:00 PM in a car parked in sun, and it just started to feel right after 20 minutes when I got there. Everything in the car was very hot to the touch. Likewise if we leave the house for a few days in summer with AC off it takes hours before the AC cycles off for first time. Beyond the air there is a lot of mass to cool down.
As to the size, I would personally try to find the model or serial number and look it up.