This arises from my own question How to handle coordinates accuracy in ArcGIS where I have tried to use the documentation entitled Using geometry objects with geoprocessing tools as a reference.
I have a table with coordinates in degrees:

I created event table and added it to the view with coordinates system 'GCS_NZGD_2000 WKID: 4167 Authority: EPSG'. I converted this single point to shapefile, defined it projection and computed coordinates of the point using 'Add Geometry Attributes' tool. This is resulting table with numbers as expected:

To replicate this in arcpy I've used this code:
corners =[[174.73,-36.76]]
p=[arcpy.PointGeometry(arcpy.Point(*coords)) for coords in corners]
arcpy.CopyFeatures_management(p, "d:/rubbish/points.shp")
I added output 'points.shp' to the view, defined projection and computed coordinates of the point using 'Add Geometry Attributes' tool. This is resulting table:

As one can see from the picture below the distance between 2 supposedly identical points is close to 10 meters:

However when I updated existing dataset with defined projection using
infc =r'd:\scratch\from_xy.shp'
outRows = arcpy.da.InsertCursor(infc,("SHAPE@","X"))
feat = (arcpy.Point(174.73,-36.76),0)
outRows.insertRow(feat)
It worked. Lessons:
- Don't use examples similar to the documentation entitled Using geometry objects with geoprocessing tools
- Define projection of dataset prior to any games with geometries.
Does the documentation entitled Using geometry objects with geoprocessing tools need to be revised?