Is double headcoverings a myth?

Back in the day when I used to ask the point in wearing a hat or a black velvet yarmulke, I used to get the same response. Besides for it somehow becoming the “uniform” of the yeshivish world- there is a deeper meaning I was told. The black velvet yarmulkes and hats create a double head covering- which apparently is needed when you daven, because yarmulkes are a minhag so its sure as hell not needed regularly.

The question is this- is there any source for double head coverings or is this a bunch of yeshiva guy urban legend BS?

Show me the source!