One can certainly cook fat up if one prefers, but that fat up 'bastes' the meat is a myth. First, exterior fat on briskets is mostly hard fat, i.e,. it doesn't render much. Second, what does merely drips off the brisket, as Noe correctly notes.
It's an individual's choice of course but fat down means the up side is protected from the more direct heat emanating from below, and it means the rub on the lean side doesn't get scraped off by the grate nor is it lost via the drippings.
I'm a fat down guy.
The notion that one should cook fat up comes from classic cooking technique. But this was never meant as some sort of basting or 'keeping the meat moist' sort of thing, despite what one reads on the Net. It's done for two reasons: one, because the meat is in a pan on the oven, the pan protects the meat from direct heat; two, because the lean on the pans bottom, along with the slowly dripping fat, will create fond on the bottom of the pan, the thing responsible for flavoring the sauce or gravy that will be made after the meat cooks.