You do realize that settlements are basically private contracts right?
There is no such thing as a "private contract". A contract, by nature, is an agreement that the state will enforce. State actions are not private. If two people make an agreement and will never disclose that agreement to anyone else under any circumstances, then a court will never see it, and it is in no meaningful way a contract.
Of course that only goes double when one of the parties is a government agency. Nothing a government agency does is private.