No, I got your point just fine. You're just missing the fact that it was largely irrelevant here. You have a bad habit of trying to tell people what you thought they meant to say. Nothing about his post suggested he meant to use "white shoe" here. His mere mention of "elite" is not at all an indicator that what he said was inferior to what you suggest. The fact was that he was specifically mentioning a type of fancy attire (incidentally, largely reserved for Royal/elite people anymore).
He wasn't trying to work the angle you're forcing here. We know people refer to prestigious/elite firms as "white shoe". That has nothing to do with anything here, aside from an unfortunate sharing of a single word among two different phrases.