It isn't any of the words on this page and I believe it started with the letter 'e' (though please offer your word even if it doesn't).
Example sentence: Because he researched what he had heard from his friends, he was able to refute many of their __________.
Factoid seems to be the closest one, but the word I am looking for only refers to a belief that is false.
I think the word misconception fits in your sentence:
Because he researched what he had heard from his friends, he was able to refute many of their misconceptions.
Misconception does necessarily mean false. Definition:
A view or opinion that is incorrect because it is based on faulty thinking or understanding.
Example:
Public misconceptions about AIDS remain high.
A myth is similar. Definition:
A widely held but false belief or idea.
Example:
He wants to dispel the myth that sea kayaking is too risky or too strenuous.
More synonyms include:
error, misbelief, miscalculation, false impression, fallacy, false notion, old wives' tale, urban myth/legend
(Oxford Dictionaries Online: factoid, misconception, myth)
While not a single word, an old wives' tale may address the OP's query.
From the Wikipedia page:
Old wives tale is an epithet used to indicate that a supposed truth is actually a superstition or something untrue, to be ridiculed. It can be said sometimes to be a type of urban legend, said to be passed down by older women to a younger generation. Such "tales" are considered superstition, folklore or unverified claims with exaggerated and/or inaccurate details. (emphasis added)
One can infer that the false believe becomes more credible through repetition.
Old wives' tales originate in the oral tradition of storytelling. They were generally propagated by illiterate women, telling stories to each other or to children.
You may refer to:
Some other possibilities, perhaps less appropriate, are:
The first 'e' word that came to mind for me was 'error' or erroneous beliefs.
Perhaps you are thinking of "espousal" - although it emphasizes belief, and not whether it is true or false.
I think that "sacred cow" is a pretty good fit. A sacred cow is not necessarily false, but the term does have a negative connotation.
[noun] someone or something that has been accepted or respected for a long time and that people are afraid or unwilling to criticize or question
Myth, urban legend, believer, sacred cow
DOGMA is the closest I can think of. It does not actually mean a false belief, it is more of a blind faith in a doctrine or belief. It has gotten the negative implication of being believed even in the face of overwhelming evidence that it is wrong i.e. Flat world society.
The closest E word I can think of would be ecclesiastical, as in ecclesiastical arguments. This also does not mean false, just religious. Though the meaning tends to be for religious descriptions, it would work for you in the context that the points have been taken on faith because the "They" people said it enough to be "true".
What you describe reminds me of Memes, although that word does not fit the example sentence (a meme is a mere mental concept while what you look for is a concrete utterance.)
Pretense seems to fit (in the sense of an unsupported claim). It contains three Es!
Some combination with parrot[ing/ed], like "parroted claims" or even the bare "he was able to refute many of their parrotings" would emphasize the repetitive and thoughtless aspect of both adaption and echoing.
How about Delusion? "An idiosyncratic belief or impression maintained despite being contradicted by reality or rational argument, typically as a symptom of mental disorder" (Oxford, not all sources mention "mental disorder").
