Sorry I've no citation, but I read a study a few years back that was similar to this study, but it's central focus was on trust, not the idea of an invisible angel.

As I recall, the idea was that primates trust their elders (at first). Especially with the higher primates, whose infants need constant care. The infants cling to their mothers with utter trust.

Add a big ole brain, and superior communication skills, and this becomes the origin of not only superstition, but religon as well.

If your parents, with all conviction, tell you that Zeus is watching, lightning bolt at the ready, for you to follow his laws; tell you stories of those that tempted the gods in the past and their ultimate, unfortunate fate; well, you believe them. Same with Santa Claus, that black cats in your path are bad luck, and about a million other examples.

How would the experiment have changed if another child informed the group that there was an invisible being in the room watching. Would they have the same level of belief?
All the study shows, in my opinion, is that humans will try to break the rules of the game, unless there is the the fear of getting caught, by either real people or invisible spirits. This seems to me a greater advantage in the early days of our species. If you don't think you'll get caught snatching that fig from your brother, why not give it a shot? The more I eat, the greater my chances of scoring with Lucy. However, the clan would discourage such behavior because of the intercine squables, and quickly establish not only rules, but stories to go with those rules:

"The dark-shadow-forest beast eats those that steal from the community hoard !"

"Santa Claus has this list, see...."

"There is a eternity of flame awaiting for you."

For what is faith but trusting what others have told you, especially those you respect, or those your very life depends upon?

I'm not a parent, but I see this in how children are raised even now. Parents tell their children tales to modify their behavior to be able to live in the family-clan-tribe-society and survive long enough to create a few replacement humans before they croak. When this fails, there is usually corporal punishment. Same with a society: violate the rules and they'll kick your ass, one way or another. "Did somebody say 'Spanish Inqusition?'"

Funny creatures, we humans. But I don't think the evolutionary path favored the fear of an invisible being that held sway over reward and punishment. It favored trust in our elders to teach us the skills needed to survive in a world that didn't give a damn if we lived or died. But the information passed down was often seasoned with crappola to explain the random cruelty of life on earth.

And still is.