Suzanne Collins paints the Hunger Games as a weapon, a method of power and with this quote, she is emphasizing how innately indestructable the Capitol's weapon is supposed to be. The games are used as entertainment for the upper-class society which keeps them submissive to the government while it also symbolizes fear and obedience among the lower class. Having the games be such a secure aspect of the society ensures the governments' rule and power will not be overthrown. It's supposed to elicit such fear among the districts that citizens don't consider the possibility of its defeat.
