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Issue with both QGIS Desktop with Grass 3.4.4 amd 3.6.0

I have two datasets: The U.S. county shapefile set http://www2.census.gov/geo/tiger/GENZ2017/shp/cb_2017_us_county_500k.zip

and the U.S. Climate Division shapefile set ftp://ftp.ncdc.noaa.gov/pub/data/cirs/climdiv/CONUS_CLIMATE_DIVISIONS.shp.zip

I'm trying to use intersection (or Union) to identify for each county, what climate division(s) it is part of.

Climate divisions do not cross state lines by definition.

With intersection, my expectation is that a county will be in one or more climate divisions since climate divisions do not always enclose a county.

When I do the intersection I get some strange results.

Vector-->Geoprocessing Tools-->Intersection, input layer is counties, overlay layer is Climate divisions.

I also have an error report of an invalid geometry so I've turned on ignore features with invalid geometries. Processing-->Processing-->General-->Invalid features filtering Skip (ignore) features with invalid geometries. There appears to be one invalid geometry in the Climate file.

Example:

Barbour County is a county in Alabama.

When I look at the resulting database from the intersection or union, I get three records.
2 of them appear to be correct in Alabama, and there is a 3rd that appears to be incorrect in Georgia.

When I look at Choctaw county, which is in Alabama, I get 3 records
2 of them appear to be correct in Alabama, but there is a 3rd that appears to be incorrect in Mississippi

Overall there are of 7,404 polygons generated by the intersection, over 1,000 which have a state mismatch.