You may notice that the grid 1238 1238 is displayed as 123 123 when using six figure grids. In other words, the SW corner of the square containing the point is used to specify it, as opposed to using the nearest intersection of grid lines.
This is correct as per the definition of MGRS. For more information see MGRS on Wikipedia.
Note that this is opposite to UTM, which is rounded instead of truncated.