More Heaven's Feel spoilers than UBW, really: Oh yeah, nearly forgot about that. The Grail's original intention was to open a path to the Root (which is ultimately the goal of most magi). During the 3rd Holy Grail War, the Einzberns cheated and summoned the Servant Avenger rather than a Berserker-class Servant. Avenger, the Zoroastrian God and personification of All the World's Evils, was horribly weak and died very early on. When he went into the Grail, he corrupted it, and over time it became his vessel. His corruption allowed for evil or anti-hero Servants (Like Medea, Medusa, Gilles de Rais, etc) to be summoned. This also made any wishes the winners would make become fulfilled in the worst way possible, usually by killing everyone and everything.
Nobody really knew this, and that's why it's considered minor. On top of them not being able to say anything about Shirou and Gilgamesh, they have to keep the story to how it is or they'll be found out. This is never really explained in Unlimited Blade Works, it's really Heaven's Feel where this comes in.