As I heard it: When BA were documenting the first 1,000 autolands with the L-1011 at LHR, the engineers noted the very small amount of scatter of the touchdown points, so they asked the airport authority for an opinion. The panicked reply caused the Collins/LearSiegler engineers to program a bit of scatter in the touchdown point.
If it were really important, I could ask an old retar'd co-worker who was one of the design engineers at the time.
GB