Quite simply, it's a plumbing code requirement.
Any time that you "connect" potable water to waste water there has to be either an air gap or a vacuum break. Should the hose be connected, and for whatever reason, the water system loose pressure, then gravity could cause contaminated water to siphon into the potable water. A backflow preventer (check-valve), if stuck open, will not stop this siphoning. An air gap or a vcuum breaker will.
2014 RAM 2500 Laramie 4x4 Quad Cab w/Cummins Turbo Diesel, 2009 Rockwood 2607, and 3 'yaks!
300W of Suntech Solar, a Rogue MPT-3024 Controller, and a Xantrex PW2000 Inverter