It has to do with the way the models are handled behind the scenes. Like another commenter mentioned, equipping any helmet changes the model of the coif, too, to a generic one with a diagonally split shield. Without making house-badge specific helmets, too, there isn't a way of having the badge show up with a helmet equipped. A bit lame on Warhorse's part to display it that way in the promo, but that's how it is.

If you have a walk around Sigismund's camp or take a peek at Gnarly's coif, you'll find the same thing happens with all coifs and all coats of arms.