The discrepancy is due to registration issue as pointed by @Vince. I checked some other places and, globe view and flat view seem to agree there quite well; which also means both uses WGS84 for the datum as pointed by @FSimardGIS.
The solution was to use proj4 string instead of the Known Coordinate System.
var Arc1960UTMZone36S = KnownCoordinateSystems.Projected.UtmOther.Arc1960UTMZone36S;
Arc1960UTMZone36S.AuthorityCode = 21036;
String proj4_21036_str = "+proj=utm +zone=36 +south +ellps=clrk80 +towgs84=-160,-6,-302,0,0,0,0 +units=m +no_defs";