Super-sleuths tracked down the rumors and put together the clues to discover that there was, in fact, another Battlegrounds Quest Reward option! This last, elusive Quest Reward is called Partner in Crime, and the Reward grants you your Hero’s Golden Buddy when completed.
Unlike all the other Battlegrounds Quest Rewards, Partner in Crime is only offered in very specific circumstances. Specifically, ALL heroes in the lobby must have a valid Buddy option (that means no heroes that came after Buddies left, like Sire Denathrius or Queen Azshara), and also nobody can be playing as Sir Finley or Elise Starseeker.
If your lobby fits these criteria, there is then a 1% chance of the lobby rolling Partner in Crime. If you do, it will be offered to everyone in the lobby.
Congratulations to everyone who helped solve the mystery, and good luck to everyone still searching for their Partner in Crime!