ArcGIS 10.2 Near 3D tool: What does zero mean in near fromxy, near toxy?

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I am running the near tool for points with different attributes. Many are in the same location, so I would expect the Near_DIST3 to be zero and the location of the nearest point to be zero. But, I also get a few points where the location of the nearest point is zero and the nearest point is far away. How can it be far (register as a Near_Dist3 -1 or over 10 meters away) and list "0" for the nearest point location (aka the points are in the same place)?



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