Looking for a word the describes a common belief is often not the case

You could try "misconception" or "popular misconception," especially if people are simply mistaken about the facts. "Fallacy" might be more appropriate for an incorrect theory or faulty logic. If the mistaken notion finds expression in a name, like "risk-free bungee-jumping," you could call it a "misnomer." If you think it results from a mistaken world-view, then I think you have no choice but to refer to it with some clumsy thing like "false paradigm" or whatnot.

I think you're looking for the word "Apocryphal".

a·poc·ry·phal əˈpäkrəfəl adjective (of a story or statement) of doubtful authenticity, although widely circulated as being true. "an apocryphal story about a former president" synonyms: fictitious, made-up, untrue, fabricated, false, spurious; More

"FACTOID" (non-American English)?

fact +‎ -oid; coined by Norman Mailer in Marilyn (1973): "facts which have no existence before appearing in a magazine or newspaper, creations which are not so much lies as a product to manipulate emotion in the Silent Majority". An inaccurate statement or statistic believed to be true because of broad repetition, especially if cited in the media.