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Alrighty, playing some Adventure Squad again. An important thing to note about the "Buddy Passwords", you can only recruit one at a time. If you enter more than one password before recruiting the pokemon the pokemon that you entered the password last for is the only one able to be recruited in a current play session, and you have to re-enter previous passwords, start up the game, and recruit them one at a time for it to work.
A bit clunky, but I suppose these were intended to be used on the day they were distributed. Thankfully entering multiple passwords does not seem to render the pokemon before the latest one unable to be recruited, you just need to re-enter the buddy password from the main menu again.