Dear Simple,
Having a white shirt rule, does not mean the Rosh Yeshiva thinks it has a meaning. Some things just are the way they are, without any idea behind them.
There is no reason to make a case for an applied meaning here. It just clothing. Just wear it. In Yeshiva one is (At least should be.) identified by their studies. The fact that their clothing was constructive at some point, does not imply anything beyond that point.
It could very well be that Rav Miller zt”l intended the opposite. The levush has no meaning. Since people tend to look for meaning in random places, he made up some positive thinking that could go into our standard clothing. His point is that they should think more. Not just dress the part.