Right, it sounds like you're used to eating meat from the flat, which is largely devoid of fat. In most of the places I went in Texas, you could ask for your brisket fatty or lean/moist or dry. I, and most people I think, asked for moist, so we got a piece from the fat end of the brisket, which had more of the meat from the point.
I've never been able to get Smoque to heed my request for the fatty bits, so I wish I'd gotten your plate.