Blender ignores a "Single Vertex" vertex group , when assigned as emitter in the density panel of the particle system. It simply emits from the all the verts.
No other modifiers are applied to the emitting plane.
Because you've set Emission > Source > Faces, and as you've painted the central vertex it considers that all the faces that this vertex is part of will be affected. So you need to subdivide your plane a bit so that only the central face will be affected.