These side-channel activities are sneaky attempts by politicians to subvert the rules that make government communications open to investigation. White House political operatives pulled the same trick by using accounts from the Republican National Committee to e-mail about issues they didn't want showing up in White House archives. (Note to bias detectors: I'm not saying only Republicans do these kinds of things. I hate this kind of behavior from politicians of any party.)
Of course, enterprise employees have long used tricks like these to get around corporate policies. For instance, IT may set up mailbox limits to encourage users to get rid of older mail. But rather than purge, users convert old messages to PST files and save them on hard drives or removable media.
As I mentioned in a previous post, that becomes a problem if your organization has retention and disposition policies -- IT may think a message has been destroyed, when it's actually tucked away on a hard drive somewhere. This also could lead to problems in electronic discovery. Users may delete incriminating messages that they have been ordered to hold, or the discovery search might miss PST files on a laptop or flash drive.
Of course, there's a difference between using a personal account for state business because you want to circumvent potential subpoenas, and using a personal account because you're just trying to do your job and IT keeps throwing up roadblocks.
There are technical solutions to the later problem, such as e-mail archives, which can make end users happy by providing an almost limitless in-box and make IT happy because they can enforce retention/disposition polices at the archive.
I'm not aware of any solutions for political machinations, other than the imperfect method of swapping out one group of sneaks for another every four or eight years.