If they aren't close, it is a good spot to take one, or the other or the average of the two to clean up the point location for good.
I'm sure you both know this, but it's important to clarify for the good of the thread that in the geodatabase you cannot pin down a location through geoprocessing; the location will change if saved to a new feature class with a different domain and resolution. Coordinates in the gdb are not stored as double floating point (like shapefile), they are stored in an internal integer grid with resolution equal the feature class or feature dataset resolution. Large database applications that want to persist coordinates must take care to have the domain and resolution set to be the same for new feature classes to avoid coordinates moving (back in ArcInfo workstation days floating point issues led to "fuzzy creep" through many overlays which is one reason Esri went with integer coordinates for the gdb). There are also performance and storage considerations, you can trade precision for data table size (and performance).
Usually we can just with the resolution and domain defaults and ignore the issue, but it can become important when managing large, high accuracy datasets through time, and, if we get into the weeds with feature manipulation as Darren has done. Setting an appropriate non-default XY resolution is sometimes needed when running spatial joins to get appropriate results, especially if two input datasets have different precision or accuracy.
I found a more complete discussion about geodatabase coordinates and spatial operators in the ArcObjects .NET help:
ArcObjects 10 .NET SDK Help Understanding coordinate management in ArcGIS
To achieve precise and predictable results using the geometry library, it is essential that the spatial reference of geometries in a workflow is well defined. When performing a spatial operation using two or more geometries, for example, an intersection, the coordinate systems of the two geometries must be equal. If the coordinate systems of the geometries are different or undefined, the operation can produce unexpected results.
Darren: does setting the arcpy.env.XYResolution improve your results? Based on the .NET doc it seems like that may help.
I totally agree the Python geometry operators documentation needs to be improved!