The Check Geometry tool detects the Self Intersections, even if distance between the feature vertices is more than XY Tolerance.
Last Published: July 14, 2015ArcGIS for Desktop
Bug ID Number
January 24, 2015
November 24, 2020
ArcGIS for Desktop
Operating System Version
After review by the development team, it has been determined that this issue is related to a known limitation with the software that lies outside of Esri's control. The issue's Additional Information section may contain further explanation.
This is by designed. XY tolerance is 0.0001. Distance between verts is 0.002. XY Tolerance is the distance the verts can move fo 0.01*2 is OK.