I think the concern people had regarding, as you call it, "media-whoring", was primarily regarding getting paid for it - not too much exposure in general. And when they made that "deal" with the national networks, and cut off the local media, who were doing much to get Lisa's picture and story out there.
And now, in addition to cutting off the local media exposure for Lisa, they announce that they'll be cutting back even more, which would be cutting the national exposure for Lisa.
I don't see it at all as damned if you do/damned if you don't.
I see it as confusion over parents of an endangered, defenseless, kidnapped baby cutting off a huge means of rescuing her, and asking themselves why in the world parents of a kidnapped infant would do that? How in the world will they find her?
Maybe they have some great secret plan that's even better than cooperating with LE (48 hour gap in that) and getting an abducted baby's picture out to as many people as possible via the media. I don't know. I can't think of what could possibly be anywhere near as effective.
How 'bout you? What plan, what means, can you think of that's better than cooperating with LE and getting your abducted baby's picture and notification that she's been kidnapped out to as many people as possible via media?