In figure 1, the black shape represents the result of intersecting the yellow circle and the gray shape. If I zoom it to 64k%, as shown in figure 2, I see a sliver of yellow between the gray and black shapes which means that the intersect tool is leaving a 'residue' which it ideally should not and therefore the result is not accurate. I've tried this on both Mac and Windows systems running 2017.0.2 release of Illustrator CC but the result is the same.
I have no stroke and the outline view of the result shows that the resultant path is not aligned with the circle.