Experimental evidence of the value of redundant oral tradition

Something I’ve been hearing a lot lately (specifically from Orthodox Jews, although it comes up a lot in debates about religion) is that having a large number of people telling a story makes it more likely the story is true, because multiple witnesses can call each other out for deviating from the truth.

My gut reaction is that this is extremely false. But it’s a point that should be scientifically testable, and I figure that someone should have done a study on it by now. Does anyone know of such a thing?

A related issue is the argument that oral tradition meant something very different thousands of years ago, when it was the ONLY form of historical record. Oral historians were duty-bound to preserve the story. This sounds plausible. It probably ISN’T as easily testable since we can’t compare oral history from pre-writing times against… well, much of anything. (Well, I guess archaeological evidence, if the events being described would have left enough archaeological evidence). Is there an official, accepted scholarly opinion on this?