The argument as used by Orthodox Jews is an interesting case study of what I think of as "unique apologetics." There's a large body of apologetics that is structurally very similar across a wide swatch of religions. However, many religions have small bits that give their apologetics a unique flavor, a way of at least superficially distinguishing their religion from others. For example, among Islamic apologetics, one sees the argument that a founder of a religion that was false would likely claim to be divine, and that Muhammad's not doing so is evidence of his sincerity/the truth of the religion.

Among Orthodox Jews, the argument of a large scale, simultaneous oral tradition dates back to the Kuzari, an apologetic series of dialogues by Yehuda Halevi from the 1100s. The argument in its most general form does sound valid: if one did have a few million lines of separate transmission this would be quite strong evidence. The problem isn't really in the lines of the argument but in the factual premises of the details. There are some aspects where the ancient Israelite oral tradition seems remarkably accurate (see for example, the genetic research about kohanim). However, there are not a million separate lines of transmission but rather a large number of people interacting and talking to each other. Now, arguably that should reduce the total amount of memetic drift (I'm possibly stretching the meme-gene analogy too far here but the idea should be clear). But the oral tradition itself is shown to be severely mutable in many respects. One amusing example of this failing is a line in the Talmud that discusses the importance of properly attributing ideas and sayings to their actual authors. An identical line shows up in multiple locations, each time attributed to a different Rabbi. This also helps answer your question and suggests that oral history can be frequently extremely unreliable, even in cases where the people in question feel a major moral/ethical duty to pass it on reliably.

Moreover, the combination of both written and oral tradition itself testifies strongly to the tradition having been repeatedly reduced to a bottleneck where at most a few people were aware of the tradition. For example, see 2 Chronicles Chapter 34 and 2 Kings Chapter 22 where under the time of King Josiah it is implied that almost everyone has completely forgotten much of the tradition until a copy of something (possibly a Torah, possibly the text of Deuteronomy) is discovered in a wall. This is not the only example of this sort of event recorded in the Bible. The Bible describes a similar set of activity at the time of Ezra.

So, the upshot is that in general it seems that oral history is not very reliable although there are a handful of striking examples of apparently accurate oral history. It isn't clear how one would tell how frequent such incidents are. I wouldn't rely on the Missionaria Protectiva.

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?

Sociologists have tested the degree to which myths and folktales in present day oral cultures vary with retellings and transmission. I'm not finding the study with a cursory search, but I recall that they found that although the tellers thought they were telling the same story each time, the stories actually changed, not just with transmission from one teller to another, but with retellings by the same trained storytellers, and sometimes in significant details. The sociologists had to pretty much dispense with the notion that highly trained individuals in an oral culture were able to effectively preserve the content of the stories passed down by word of mouth much better than individuals from cultures used to using the written word would be able to.

More people confirming a story is certainly epsilon more evidence that the story is correct (Because more people confirming a story being evidence that it is false is absurd).

A more interesting question is, what is the magnitude of epsilon in a case like the one described here? This is in principle testable, but I certainly don't know exactly how to go about testing it.

A better way to correct for errors in transmission of a body of knowledge (including stories) is to write the knowledge down (i.e. encode in a "dumb", semi-permanent physical substrate), rather than rely on oral re-tellers to identify each others' deviation from the average re-telling.

My gut reaction is that this is extremely false.

Funny, my gut reaction is that this is extremely true.

If 1 or a million people tell me some thing, there are exactly 3 options available to me:

1. increase my belief in that thing by some amount
2. leave my belief unchanged
3. decrease my belief

Suppose my 50 neighbors - all nice normal folks - tell me in passing that they saw my brown dog loose in the morning. Why would I decrease my belief? Wouldn't that be incredibly perverse?

And why would I ignore them and leave my belief unchanged? I don't discriminate against any other information source. If my eyes tell me 50 times that my brown dog is loose, I don't go 'phsaw, who cares what you guys think'. I increase my belief that my dog is loose.

About any proposition in general, the more people tell you it, the more you believe it. Let's generalize this even more: the more data you have telling you to believe some proposition, the more you believe that proposition. (What a shocking conclusion.)

Now, sometimes there are conspiracies, but they are extremely rare and unlikely and require involved explanations (like explaining the existence of religious belief in general does). Those Jews are right that the more testimony the greater the likelihood, but this truth does not prove the things they want it to prove.

tl;dr: your post is ill-founded and you need to explain why the Bayesian solution to the raven paradox is wrong.

Which people are being referred to in your first paragraph? The original people writing down the books? Because there are contradictions in what was passed down.

Or are they counting just anyone who believes what they believe? Because then we have to get into independent evidence vs. non-independent evidence.