This is a wonderful example of a question that has no “Yes” or “No'“ answer because of the problems of language.
Dictionaries will commonly give multiple related, but distinct definitions for the noun ‘myth’.
This is simplest so we’ll start with it.
a commonly held but false idea - Cambridge Dictionary
any fictitious story, or unscientific account, theory, belief, etc. - Collins English Dictionary
any invented story, idea, or concept - Dictionary.com
a widely held but false belief or idea - Dictionary at Google.
For this meaning of the term ‘myth’ it therefore necessarily follows BY DEFINITION that all such myths are necessarily fictitious and false.
Example:
Men are better drivers than women
Under most normal driving conditions this has been established by numerous studies to be a myth.
The point here though is that we only know it’s a myth once it has been proven / sufficiently evidenced to be a myth.
Myth Busters tested hundreds of myths and found, often to their surprise, that some of them turned out to be true. At that point, under this definition, they cease to be myths.
This leads to an uncommon example of one of my favourite subjects, a paradox.
There are many myths which are widely believed to be true, and which are widely believed to be myths because they aren’t true, but which turn out to be true, and so are not myths.
One can dispute whether this is a genuine paradox or just a self-contradictory statement. How can something be widely held to be true, and be widely held to be a myth / false statement, at the same time?
And yet, for the example we just gave about men and women drivers, it does seem that this is the case. The myth that men are better drivers / navigators than women appears to be widely believed to be true, and yet it’s widely believed to be a myth because it is actually false.
Human’s are perverse and illogical and that term ‘widely believed’ can cause us lots of problems.
Now let’s have a look at the other major meaning of the word ‘myth’, the one more commonly tied in with the words mythology and mythological.
an ancient story or set of stories, especially explaining the early history of a group of people or about natural events and facts. - Cambridge Dictionary
a traditional story of unknown authorship, ostensibly with a historical basis, but serving usually to explain some phenomenon of nature, the origin of man, or the customs, institutions, religious rites, etc. of a people: myths usually involve the exploits of gods and heroes. - Collins English Dictionary
a traditional or legendary story, usually concerning some being or hero or event, with or without a determinable basis of fact or a natural explanation, especially one that is concerned with deities or demigods and explains some practice, rite, or phenomenon of nature. - Dictionary.com
a traditional story, especially one concerning the early history of a people or explaining a natural or social phenomenon, and typically involving supernatural beings or events. - Dictionary at Google.
The discerning reader has probably picked up by now that the dictionaries are having a bit of trouble with this word ‘myth’. And to be fair to the dictionaries this cutting and pasting isn’t fully appropriate here because several of them include numerous shaded definition of the word, not merely two. That’s one reason I’ve included the links.
But it’s also clear that we’ve run into some problems. For example, the definition taken from the Collins English Dictionary above, specifically includes the words ‘of unknown authorship’. That’s a curious inclusion. There are numerous books of The Bible for example, where the authorship is clear, numerous books where it is disputable, and some where it is indeed ‘unknown’.
Homer’s stories about Troy / Illium, Ulysses / Odysseus, and Atlantis are / were widely considered to be mythological. However the author is very definitely known. (Or is he? Some suggest that Homer is not just a blind story teller, but a composite character).
Notice too that the definition from Dictionary.com clearly includes the phrase ‘with or without a determinable basis of fact or a natural explanation’.
This makes explicit an issue the other definitions omit, that myths may or may not be fact or fiction.
Time for a reasonably authoritative quote:
To say that a story is a myth is not to say that it is necessarily fictional. Greeley, Andrew M. Sociology and Religion: A Collection of Readings (1995)
Now Homer’s story about the Trojan War and the subsequent Iliad - voyages of Ulysses / Odysseus were widely believed to be mythological works of fiction until the discovery of the ruins of Troy in 1870 and the subsequent excavations that disclosed the size of the city.
At this point Homer’s story moved from being fictional mythology to being:
historical fact,
historical faction,
historical fiction,
pure fiction with a few facts included,
or what?
Did it cease to be mythology?
And where did that leave the other stories of the Odyssey, and Atlantis?
Most people will continue to consider Homer’s works as part of ancient mythology, but that doesn’t mean they may not include some historical accuracy as well.
At which point we could throw in another word of mixed meanings that is also sometimes a synonym for ‘myth’, ‘legend’. Readers can research that word in the dictionaries for themselves.
I’ll just leave off here with a couple of other examples of ‘myths’ that turn out to be true.
There was a ‘myth’ about a creature that would swim up the penis of a man standing in the waters of the Amazon River.
Turned out it was true, there is such a creature. Science eventually discovered it. It’s called Candiru or vampire fish. It swims upstream against a flow of urine and lodges itself within the penis. Removal is somewhat difficult and unpleasant. More commonly it attaches itself to the gills of other fish.
There are numerous myths about the Bermuda Triangle. There aren’t necessarily any mysterious forces at work, but most of the disappearances are entirely factual. There are lots of seafaring myths and lots of disappearances at sea. The Mary Celeste is one well known one, which Wikipedia includes under myths, although it is entirely historically factual. The myths relate to stories, theories and ‘explanations’ of what happened that caused the crew to abandon the ship.
There’s plenty of others. One could write a whole book about them, and I suspect there are such books.
The Lost Pyramid myth also turned out to be a real pyramid. See Pyramid of Djedefre.
And there are indeed more secret chambers in the Great Pyramid. Link.
So the bottom line is that at least some myths are also true. Whether that means they then cease to be myths is for the reader to decide for themselves. But I would counsel all wise persons to keep an open mind about the status and truth of ‘myths’ until the evidence is properly assessed.