In order to build a vPro Capable PC you need 2 building components:
1.vPro Ready CPU (i5 or i7 mainly Standard and Low Voltage models with S designation) like i5-3570, i5-3470s, etc
2.Series 6 (DQ67EP, DQ67SW) or Series 7 (DQ77MK, DQ77KB) Executive Intel Desktop Boards or Q67 - Q77 in general.
Thus your findings are correct. Core i3 are not capable of supporting vPro even if you install them on a vPro Capable board.
You need both building blocks to be vPro ready.