Well, it's actually just that Adidas and Nike only make most of their shoes in D width, so people with D width CAN wear TTS (bannock) but people with E or EE or EEE width need to size up for comfort or so their feet aren't actually coming out of the sides of the shoe.
I measure 8E and I wear 8E in everything dressy like Allen Edmonds Gucci etc. I wear 8.5 or 9 in Vans, Nike Adidas etc - 8 won't even get my foot into the shoe sometimes.
So when people say "Size up or size down or TTS" and they're talking about Nike or Adidas, they usually have no idea what their talking about since they've never known their measured TTS Brannock size or worn a nice dress shoe in their life.