Morality for Appearances and the Ring of Gyges

In Plato, Republic Book II, the Ring of Gyges is a mythical artefact that allows the wearer to be invisible.  With invisibility granted by this ringer the wearer acted in an immoral way.  This was an example for the argument that people act morality not for an intrinsic morality but rather the appearance of morality as it instrumentally served them.
Psychologist Daniel Batson of University of Kansas did a series of empirical studies showing that students would 80% of the time be self serving and rate their morality in such cases as 4 on a scale of 1-10.  However if they were allowed to flip a coin and then do a self serving deed, this appearance of being 'reasonable' ie flipping a coin, resulted still in them acting selfishly 80% of the time but because they had taken the time to flip a coin, even though they ignored the results, this resulted in them seeing themselves as acting reasonably and justly, and rating themselves 6-9 out of 10 on the scale.
If a simple action such as putting a mirror facing them on in another experiment putting a pair of eyes was introduced people act less selfishly and more fairly.  The evidence is that most people act morally out of fear of shame.
I'm interested in the 20% who indeed appear to act morally from some more deeply seated sense.
However this speaks to the need for transparency in the courts and certainly supports the idea of television cameras in the court room at least for the masses.  We do this in parliament and despite back room deals this openess probably promotes greater morality.