I voted that they are blinded by family loyality. There is, of course a lot more to it than that, but it was the closest I could come, given the choices. As JustJax pointed out, they are "untruthful, combative, control freaks, and I will guess anti social. From what we have seen they have no social circle, no family and or friends speaking to demonstrate they are anything other than they have portrayed themselves to be....hostile, agressive, disingenuous people."
I remember early on, when they were holding vigils in their driveway, it was mentioned that the only people permitted to attend were those that believed Casey had done nothing wrong and that Caylee was alive. They are the type of people who believe that if you are not 100% in their camp, you are "against" them. This attitude is why they have ended up estranged from family, have few friends, and are isolated to a large degree.
IMO, their grief over the loss of Caylee has not made them change any of their ways. Indeed, they have lost a priceless member of their family and don't want to lose another.
So... they don't listen to sound legal advice. If they had, they would have never continued the media-thon. Mr. NeJame was intelligent enough to leave them when he could not deal with them. Mr. Conway should think long and hard at what type of legal work he has ahead of him.
They have harmed Casey's situation beyond belief. They have lied to LE and the media. Those lies will haunt them on the witness stand when they are revealed. Anything they have said in the media and in the depositions WILL be used against them and Casey in a court of law if necessary.
The best way they could have helped their daughter would have been to keep their mouths shut.