MM fell off a balcony / behind a couch / off a window sill 'had an accident' whilst drowsy, wandering, crying, looking for mummy, having being 'drugged' (sedated) by her parents who like to go out for a bevvy with their mates.
A cover up by Kate and Gerry and all or some other members of the Tapas group ensued, all fearing reputational damage / careers threatened / legal action, with some or all also 'sedating' to go out for a bevvy. They've all shit themselves and, probably after heated debate with a couple of dissenters, a pact was formed which evolved quickly.
Coincidentally, one of the group, Mr. Payne, was known to have odd proclivities and was oft reported making lewd, inappropriate gestures. This had no bearing on the incident or subsequent actions whatsoever. It's just that there's usually a wrong 'un in each large group.
Did I hit all the bases? Plausibility is subjective, so don't come back with 'sounds implausible'. Shannon Matthews - probably deemed to be impausible right up until it wasn't, for example.
Jesus, that looks like Dav typed it! I'll fix it.