Supertorso wasn't made with a lot of respect, so I'm going with that.:)
The only handwaving you might do, is that just as many JLA DID know Bruce's identity BACK in the day, they knew Barbara Gordon was Batgirl. Barbara's assault by Joker was public news, so it might've been expected to be occasional gossip. Oracle was the big secret, and one Barbara wouldn't have wanted connected with herself. You'd think she'd have a clinical account of Batgirl's 'retirement'.