I'll sound like your college English teacher here, but the answers are citations, primary sources, and more citations. Telephone (as I know the game) "works" because you don't know what the person telling you something was said. This is easily avoidable in an academic text. Citations allow you to see where every bit of information is coming from so you can verify its accuracy.

If I'm writing a paper on a Latin epic poem, I'll have the commentary or secondary scholarship in one hand and the Latin text in the other. A good text or commentary will even have notes of all the times different Latin manuscripts vary. If the book claims a line's meter is weird, I will read the text to make sure that's true. If they claim a word is only used in a single stanza, I can search an electronic text. If they make a brief statement from another scholar, I can go read that scholar. If they reference an inscription on a tombstone, I should be able to visit that site or museum and read that tombstone for myself. Ideally, I should be able to recreate this person's research and come to the same conclusion or, if I disagree, solidly explain why.

It should not be the case that "people continue to reference pieces of history off of new sources." If I'm writing about WWII, it's good for me to use other people's research to save time. But I should also be referencing as many primary sources as possible. And if someone's research doesn't mesh with what I've found, I should not be afraid to question them. There are military records and firsthand accounts by the score, so there's no need for me to reference someone else referencing them, especially if they are crucial to my research.

There ARE major shifts in interpretation, or changes in theoretical approaches, and some of them have quite an influence on the field. For instance I'm working on Roman Imperialism (the expansion of Rome from a city-state to a city-state ruling the Mediterranean, not the Roman Empire), and different scholars come up with different answers - defensive imperialism (very ancient) is the notion that Romans fought almost exclusively defensive wars and accidentally ended up with an empire. Aggressive Imperialism is quite a bit more recent - Harris I think is the scholar for that one - Romans were an excessively violent culture that the rest of the Mediterranean couldn't keep up with. There are also arguments people make about Rome's imperial drive being a function of internal elite competition, or it's a function of Rome's position in the international community. But all the good scholars presenting these positions give their primary evidences for them.

So we go back, look at the primary evidence, the arguments that scholars make agreeing or disagreeing with the position in question, add any ancient evidence we think an author missed, and evaluate the argument.

There are two places where this doesn't happen. First, if you're trying to trace the development of an argument over time. In that case you want to say something like "Beloch in the 19 century argued from such and such evidence that the Roman population in the first century amounted to only about 5 million, but thirty years later Frank reinterpreted the same evidence and arrived at a figure of 12 million." A complete investigation of the primary sources here isn't useful; the point is to trace the theoretical evolution of the field; a concrete instance of this kind of thing that's important for me (if not for anyone else), I think if you're reading Syme's book on Augustus, it's incredibly important to remember he published in Europe in 1939, and totalitarianism would have been something he was thinking about and maybe could help explain why he disliked Augustus so much.

The other place is in pop histories (I include Dan Carlin here). Those are not meant for research. They sometimes discuss their sources or their intellectual influences, but they're really story telling.

If you never went back to the sources, you would be playing Telephone.

I can't speak for all historians, but I try and review the archival documents even of things that have been gone over many times by many people. The reason is that my eyes are not the eyes of the historians who read them before me, my questions and concerns are not their questions and concerns, and my interpretations are not their interpretations. This is separate from the question of the operator game, but in the process of doing this I've discovered a great many things that have just been repeated and repeated by even very good historians but turn out to either not be true, not be the whole story, or not actually be known.

Just as one very small example of this from my research: the fact that Kokura and not Nagasaki was the primary target of the second atomic bomb is well-known. The Kokura strike was abandoned after clouds of some sort obscured the visual targeting. This is usually remarked upon without much interrogation by historians writing about it. However I noticed that there were at least three different, not entirely compatible explanations for the clouds being cited. Apparently nobody else seems to have noticed that this detail has never quite been ironed out, and it has important implications for understanding both Kokura and Nagasaki's respective fates. This was an issue I spotted using secondary sources alone and noting their incompatibilities, which is one way to attack this problem.

Generally I try to go to the original sources whenever it is practical. Often I find they are quite different, or more complex, than the secondary narratives derived from them. I am sure some future historian will look at the same sources of mine and find things I missed. It is one reason not to be overly consumed with the vast literature of secondary source work. Scholarship is important to keep up with, and provides necessary context, but working exclusively with secondary sources leads to accrued errors and can strangle originality.