Well...
...the obvious main point to this is COH's reference to FOIA. There are and always have been, of course, governmental documents and communications which are exempt from FOIA. But that's not something left up to the officeholder themselves to determine. There's a process in place for it.
And, besides, something being made public and something being subject to interbranch oversight and review are two totally separate things.
James Carville screwed up when he admitted (or, at least, speculated...given that he wasn't officially speaking for HRC) on national television that the reason she did this was to hide things from congressional oversight.