I have traced the outline of an area in Google Earth. Having saved the KMZ I've converted it to a shapefile and then reprojected the shapefile to Arc 1950 UTM 35s (using transformation 8). My data frame is in Arc 1950 UTM 35s. In the dataframe properties I have set a transformation to WGS84 (using transformation 8).
When I add the basemap "World Imagery" (which comes in Web Mercator Auxillary Sphere projection) everything is fine. See below:
However, if I choose the "ESRI Imagery World 2D" basemap (which comes in WGS84 projection) the shapefile and the basemap no longer line up. See below:
Why is this?
As a further test I have started a new MXD. I've brought in the ESRI 2D basemap which has set the dataframe CRS to EPSG 4326 (WGS84).
I've converted this new shapefile to a KMZ and this is what it looks like in Google Earth:
Again the offset is ~70m.