I believe there may be a bug in how Intersects() evaluates point against polygon boundary. I went on lengths about it here <https://gis.stackexchange.com/questions/258416/gdal-intersects-not-working-as-it-should>, but long story short if you Intersects() a point with a polygon boundary, it returns False, where it should be returning True. Disjoint() also returns False. However, Intersection() correctly returns the intersected geometry (the point itself).
This is in GDAL 2.2.1, 64-bits for Windows. A user in the aforementioned post mentions it working in their 1.10.1 version.
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