Bailey cites "studies that find that invoking an unseen watcher enhances moral behavior. In one amazing experiment, when participants were told that the ghost of a dead student was haunting the experimental room, they cheated less on a computer test. Other researchers report that when experimental subjects were primed with religious words, they cheated significantly less on a subsequent task. Similarly, Norenzayan and Shariff found that subjects in experimental economic games were more generous when God concepts were implicitly activated before play."
I'm sure this happens. But here's where Christianity distinguishes itself from other religions. As a Christian I follow God because of what God has done for me, in history. Personally, the idea that I'm more moral and nicer now then before I became a Christian because "God is watching me" has rarely been something I've thought of. Instead, when I have thought about the omnipresence of God and "Christ in me, the hope of glory," I end up thanking God for how much he loves me and accepts me in spite of my failures.
But now to my philosophy of religion point. The concern is truth, and truth is a property of statements. The philosophy of religion truth-question is: "Does God exist?" If God exists and is omnipresent, then persons who believe this is true will likely be more generous. But that people seem more generous as they believe in an omnipresent God, while it may be a sociological truth, has no effect on the discussion about God as it takes place in the philosophy of religion. And if someone tries to use this to discredit the idea of belief in God or as a way of explaining why people believe in God or maybe invent "God," that's an example of the genetic fallacy.