Once you have the POINT_X and POINT_Y of points and the NEAR_X and NEAR_Y in the same table (as I decribed in the beginning), you can use the XY To Line tool with the default Line Type - Geodesic, if you have ArcGIS 10. This tool creates a line using the two point coordinates in each row of your table.
Please be aware that the line created by this tool is a geodetic line - a curving line along the surface of the earth - not a planar line; and it is densified with many vertices. Theoretically there is a difference in length between the geodesic line and the planar line between two points, but at this level of detail, that difference is ignorable. You may also use the Generalize tool (Editing toolbox, Editor license) with a reasonable tolerance to remove the unwanted vertices, so that your lines become two-point straight lines. To avoid mis-use of this tool, we might consider developing a different tool in the future for creating planar lines between two points.