The issue I see in the Chippie though is if a non-return valve fails and you roll/bank the aircraft, you risk losing a tank-full overboard. With no "Both", this can't happen in a PA28.
For comparison to the above, this is what you get in a typical Archer POH:
No non-return valves fitted in the PA28 series. I've also heard some say non-return valves can get stuck and get you in trouble but not sure how true that is.. Maybe it's simply a cost thing?