"False" warchief are not the right words. The story is explained from the view point of the winners, so the losers always had the "wrong" king, or the "false" warchief.It's even more funny when you realize that the Warchief title has only existed for 60 or so years, and has only had four people in the seat (Blackhand, Doomhammer, Thrall, and Garrosh). That's if you don't count the "false" Warchiefs like Rend and Kargath. That's not exactly a huge amount of people to set a "orc only!" pattern with. It's just orcs were the race that founded the title so obviously they would be the ones with it until the Horde became more of a brotherhood as it is now.
The had the same rights like Thrall to be the warchief. But Thrall won the war, so the others are "false".