Duplicate points are not an error, but duplicate vertices are. However you can only have vertices in a polyline or polygon, so there is nothing wrong with your sample. To find coincident points you need another tool.
It is not a useful thing to have any featureclass using play coordinates in the range 0 - 10 to test this sort of thing because of rounding errors during storage using integers and offsets. It is recommended that you always have a coordinate system defined and use real coordinates such as UTM with lots of figures if you are going to stress test Esri algorithms for bugs.
There are lots of issues with the interpretation of valid geometry between systems that check geometry does not report. See FME for a more comprehensive testing tool. Something that is valid in Esri may not be allowed in OSGeo simple features. For example a vertex may be allowed to touch the edge of the polygon or not. Why not repair geometry instead of just checking it?
The main issue that repair geometry handles is polygon vertex order is back to front in KML sourced polygons that need to be reversed to be Proper Polygons in ArcGIS.
thanks for your response. In other contexts, the terms vertex and point are used interchangeably, so it helps to know that the Esri documentation on this tool only uses the term 'vertices' to refer to line segment/polygon edge endpoints.
What I'm really trying to find out is if this tool ever gives anything other than an empty table. I'm looking for a sample broken dataset to see the Check Geometry in action. I have tried to create some 'errors' (e.g., bow-tie polygons), but I can seem to get any response from this tool.
Have any of you come across a dataset that gives more than an empty table?
Do any of you have on hand a sample dataset (that you could share) that gives more than an empty table?