Similar thing happened in Wichita in November. Pilot of the Dreamliner was talking to McConnell Air Force Base air traffic control, but landed at a much smaller private airport. It also took off without incident. The pilots were talking to McConnell, saw the smaller airport, assumed it was the right one and landed there. I theorized at the time that probably the pilots thought, "Wichita? How many airports can there be?" and assumed there was only one. In fact, there are at least 4. Three of them are roughly along the same street, including both the intended airport and the one where they landed.
Again, I wonder if the Southwest pilots just assumed Branson only had one airport and landed at the first runway they saw. In both instances, they had to be disregarding their instruments. Just glad in both situations they were able to get the planes out without incident.