We figured out today that the count overlap GP tool is by default too sensitive when it comes to counting what is "overlapping" and we've been getting some wrong data all this time, unfortunately. Snapping tolerance seems to be unable to hit the same precision and so when things snap, they will appear snapped unless you zoom all the way in to 1:1 and it'll be off --in our current case-- 2mm which is outside the XY tolerance and thus not considered snapped by the tool. The resolution/Tolerance on the source layers appears to be the default sub-millimeter (0.1mm) which is accurate far beyond what we truly need (I think we only require <1 foot resolution). I seem to be able to fix this issue when running the tool by changing the XY Tolerance and XY Resolution in the environments tab of the GP Tool which is great but I happen to normally call the tool within an arcpy script. From a quick search, it doesn't seem like those variables are exposed in arcpy? The documentation mentions that arcpy.env.XYTolerance for example affects the output Feature Class (and not the input).
What can I do outside of getting the client to manually change the tolerance on their FCs? Can I temporarily set a greater tolerance in the code like I can with the environment tab of the GP tool?