Mervyn,
Kory and I got together and we've decided to log a defect for this behavior.
BUG-000120695: Intersection Snapping Not Locating Vertexes in Multi-Part Polygon in ArcGIS Pro
Something is definitely off there between Pro and ArcMap. Do you want to be attached to this defect? If so, let me know and I can do that.
Thanks for working with us on this and let me know if you have any questions.
cc Kory Kramer