They do not like the results for parallel pipes within 90m, nor do they like how one pipe's obvious buffer could be assigned to another.
I think you had the right intuition with the voronoi. The problem as they flagged it, was that you relied on a single centroid per line segment. This made the boundary grossly jagged between parallel lines and converging segments.
I did a quick test where I took your lines and ran a Segments=5 through the transform bar, followed by creating resulting points from the lines. Then assigning the lines.ID to a LineID field in the separated points layer, I re-ran a voronoi diagram with much finer grained results that may have appealed to your clients. I am not saying this is perfect as there may be questions with endpoints that I didn't address, but it *should* give an evolving answer to either narrowing or rejecting your approach to solution.
By using a raster and determining distance from each pixel to the closest line segment you would be achieving something similar. It is still only as precise as the raster cell size, but achievable both in Mfd vers. 8 & 9. The vectored avenue allows for more data to associate with an area than a pixel cell value.
Attached is a modified version of your file. I left the slices of voronoi area in place, rather than dissolving them by LineID to show the work.
<internet failed me at this point and will probably post later, hopefully with no duplicate messages.>