Yes, that would be very difficult.
But if you're saying that the media campaign is a tiger rather than the McCanns themselves (even if they unleashed it) are you saying it's not a deliberate cover-up?
The first obvious untruth concerning what happened to Madeleine was the forced shutter/window told to family and friends, there's no doubt about that. I'm pretty sure it was a private cover-up, the people who count for them had to see them as victims. I don't think they were aware to start a global cover-up.
Unfortunately the family and friends were so convinced (and I would have been) that Madeleine had been abducted and so frustrated because they couldn't act that they alerted the media repeating the story of the jemmied/smashed/broken shutter/window, a story that left absolutely no doubt about Madeleine's fate. This is how started a rumour in which the McCanns were caught before they could realise what happened.
They could have denied it tough, but they didn't, the private cover-up was gaining worldly dimensions by proxy, too good!
With a bit of imagination they would have understood that they were passing the point of no-return.