I guess Malva could have done that, meaning whatever deal her and Looker made wan't her secret of membership. But the way that they acted didn't seem that was the case. If that was the case why was Looker so opposed to making a deal with Malva? He would know if she turned herself in meaning asking for her assistance would be a tool instead of a last resort which was how it was presented.
And her career and possibly even life being ruined by being revealed to be part of Team Flare is obviously why she'd want to hide it. I don't think there was ever a question why she wanted it to be kept secret from the public.
I meant more that media sensationalism as a career-killer for Malva, whether the accusation was true or not (just watch tumblr go wild on completely false rumors, it's not that hard to start a riot from a lie).
So in my theory:
Malva, seeing Team Flare going down, does the sensible thing and turn herself in, exonerating herself with a plea-bargain.
Looker, worried about his missing sorta-adopted-daughter of 3 days (yeah, not much sense there, but it's my wacky fan-theory), threatens Malva to go back on their deal by outing her Team Flare involvement to the public, which could ruin her career even if the rumors are denied by herself or the police (being completely true is just the cherry on top). He's initially reluctant due to this cowboy-cop tactic being on the gray side of unethical, but worry for Emma prevails.
Malva relents, and gives up even more classified details about Xerosic, but stubbornly with much outward resentment that gets directed at the player when you confront her.
Completely from my head and with little game support? You betcha'! But it reads more like a detective novel and (in my head) explains why Looker gives up the Kalos detective branch and leaves so easily in the end (guilt of resorting to unethical behavior to solve a mystery).
But as pointed out a while ago, Pokemon law enforcement makes no sense. Archie, Maxie, Malva, and many more would be jailed flat for their crimes (ecoterrorism and working with a known criminal organization/funding terrorism) but despite facing certain doom, the boy in the pokemon center just cares about his shorts and his rattata.
I digress.
In other news, it looks increasingly certain that the new green snakey thing is related to
Zygarde, based on the latest Corocoro and Mega Evolution special trailer. Specially since you get a look at their backside, where they have
a hexagon pattern.