Okay, but it still makes sense that Lois would want to check it out on her own, to find out why Katarina was so desperate to have Oracle exposed.
I kind of read the whole scene as Lois showing off a bit, trying to make a purported mastermind sweat a little, but not intending to do any real harm and already having decided not to run the story. And Babs, who doesn't necessarily know how much Lois and Supes chat about the JLA (on top of already being paranoid and irritable), is suitably prepared to show off her creepy skills with that photograph.
Basically, it's two women whose occupations are to wield information like a weapon facing off to see what the other is made of. And considering that they later become allies, I feel like this is almost a "first we fight, then we become best friends!" kind of scene.
Also, I think I just really enjoy Loisdickery and Babsdickery.