Use the attached template table instead. I adds two sets of From and To fields for line segments. One set is the full length of the segment between points on the line. The second if 1 meter short of that length at both ends. Use the Make Route Event Layer with the FROM_M_2 and TO_M_2 fields and then Spatially Join those segments to your cut up buffers. Because the lines will not touch any segment but the one they are within the Spatial Join should assign the attributes of only one segment to the buffer portion. Then you will know what linear portion of the pipeline each buffer segment represents.
The Spatial Join must occur after the buffer is segmented and before you intersect the buffer segments with any other layers.