2CubDad,
There is one thing you must know. The Order of the Arrow was founded in 1915. The Cub Scouts was founded in 1930. When the OA was founded, Cub Scouts did NOT exist.
Secondly, the Order of the Arrow, like Scouting in general, is meant for the YOUTH (Boy Scout Age).
Thirdly, in order for an adult be elected, they MUST be a registered member of THAT SPECIFIC UNIT.
Scenerio (fiction): Mr Daniels is a Member of Troop 123 as an Assistant Scoutmaster. Troop 123 is having their election tonight. An adult member of Troop 123 recommended Mr. Daniels to be called out at the OA ceremony. Troop 123 is sponsored by the local Baptist Church.
Here is Mr. Wright, a Cubmaster of Pack 987. Pack 987 is sponsored by the local Catholic Church.
Finish the story, how can Mr. Wright be tapped out if he is not a member of the Troop?
Oh, by the way, in my youth, I served as my local Chapter's Secretary.