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i've just decided you're all wrong and the actual funniest scenario of the league not knowing bruce has kids until they take his place as batman during league meetings is the scenario where bruce never even asked them to pretend to be batman.
when he can't make an important meeting he sends either jason or dick in his place just as themselves, because if he can vouch for them as proxys then why would the league have an issue with it? they just need to show up and say they're there to take notes for batman or something, there's no need to lie. he doesn't even realise that his identity is being stolen until he shows up after a meeting he sent a sub in for and when he shows up everyone is staring at him awkwardly.
batman: what's everybody looking at
green lantern: nothing! we're just... concerned.
flash: yeah... how was your surgery?
batman:
batman: what surgery
green lantern: ...well you ran out of the meeting last week yelling about how you were going to be late for your 'piles removal operation'
green lantern: so uh. how'd it go big guy?
batman:
batman: i wasn't here last week. jason was.
the league:
flash: who the fucks jason
batman:
batman: *slowly turns to superman, who is staring at the table stubbornly*
batman: clark-
superman: THE KIDS SEEMED SO EXCITED TO DRESS UP, I DIDN'T WANT TO BE THE BORING UNCLE AND SAY NO!
bruce ends up calling jason in front of the league to demand an explanation and clear his name. jason straight up doesn't even remember what he did.
jason, on call: oh hey B, thought you were at a JL meeting this afternoon?
bruce: i am. what happened last week?
jason: i sent tim the report to hand over already! i didn't get all of it though, i had to leave real quick towards the end because damian was threatening to set my safe house on fire if i didn't pick him up from school
bruce: and the league let you go early?
jason: yeah i made some excuse, i think i said-
jason: *pauses, remembering what he'd done*
jason: oh my god
bruce lays his head on the table while jason laughs through the loud speaker for the next eight minutes.