It's hard to answer any of this without knowing how the heck she got that head injury.
I don't think anyone actually thinks "Oh, the DA will cover this up no problem!" unless they are the DA's kid or the President of the US or something. The Ramseys weren't that influential. I could see them thinking "No one is going to believe we would beat our child, so if we say this was an accident, who will question it?" Or if, say, Burke hit her, I could see them thinking "They'll believe it's kids goofing around if we say that." I think many families would believe they could convince the DA something was an accident if they had always seemed presentable and respected.
One of the issues I have with RDI is that the injury was not visible and she was not dead. The crazy staging seems like such a leap. I know it's possible they heard the skull crack and knew it was bad, but I just don't know. And I know it would be possible to mistake her for dead, but it just seems they would have tried a bit more to save her and play it off as an accident at that point.
Obviously one issue was the sexual assault, but the evidence on that is still a bit murky so I can't quite figure out how that played out.
And I just don't know how you would present it to a jury and explain what actually happened. Such a strong head bash but no one knows exactly what happened. This isn't a situation with a crazy beating or shaking injuries or something that you can say was definitely the parents losing control. It just seems like there would be doubt.
Also, I think people would be very surprised at the conditions of many people's homes, at least at some points in their lives.