The "justice system" is a third party.
No. Members of a government need to be auditable. Thats why there are so strict laws and regulations about government communication preservation. Both for historians, and more importantly, the press. Just look at brazil how well it works there (compared to the US), only possible because the press has hard proof about the corruption.
This auditability is ensured on infrastructure that is given to government officials. Although it can be manipulated inside the government, that's much harder as if it were on a private server.
It's just as likely that the NSA or some other US government entity hacked her server.
I doubt that the NSA or other agency wants to do actions against one of the higher ups. They are designed to follow their commands, not to spy on them. If they hack the politicians, their practices will just be questioned far more likely. Of course, if there is a judicial order, they will act against them, as they should, but not without one.
Or is the claim that she wiped the server in such a way that it is no longer readable by the US government or even "God", but somehow can still be read by foreign governments?
No. But even the most secure form of wiping doesn't help you if someone hacked and downloaded all data before you wiped. It does help you however if the public demands access and you fear whether the FBI might turn up and seize your computers in the future.