The central area of a Morgan is a lower stiffness one due to it being a low point in the structure with far less built in bracing/triangulation. Just think.......the link from front to back is below the door consisting of chassis, rocker/sill, door frame. Closing the door could well help stiffening up!
Compare it to the triangulated chassis of a Caterham. No door so extra steel sections to give a box shape, hence improved stiffness. You step over the side to get into the car.