The error message that
VectorPlot3D[{x, y, z}, {x, -1, 1}, {y, -1, 1}, {z, -1, 1},
VectorPoints -> {1, 1, 1}]
produces
suggests that two is indeed the minimum number of VectorPoints.
VectorPlot3D[{x, y, z}, {x, -1, 1}, {y, -1, 1}, {z, -1, 1},
VectorPoints -> {2, 2, 2}]
