As a Scout, I wouldn't want to take credit from something I didn't actually earn or deserve. I wouldn't want to encourage a Scout to do that either. Becoming a member of the OA merely due to a clerical error made during a call out ceremony is meaningless and should not be what that honor represents... but sending a Scout back to his campsite humiliated, disenfranchised and in tears due to an adult's mistake is hardly what the Scouting program should stand for either.
In such a situation, I would explain to the Scout what happened (off to the side, to avoid any public embarrassment), and I'