There are many ways to acquire historical knowledge about the past, manuscripts are just one of them (they even check lice dna). Naturally not all text have same value, for example sale record tend to be most accurate, while stories suffer from unreliable narrators prejudices, biases and or limited perspective of the world; so it is best to have several text from different sources to unravel the past. This might seem obvious, but for a long time people ascribed greater historicity to their stories (particularly those they relate to, define or have faith in) by virtue of "mine is better" with nothing but their faith guarantying its truth and value.
As slave to Armok, or someone who watch fake-news on tv, one should know that a good story don't have to be "true" to sway people. Greek stories have had huge influence on culture and their traditions of story telling still pervade in our daily life, regardless of the extent of their stories historical basis, which btw isn't much if Homere epics were a movie it wouldn't be a documentary but tagged between fiction and
based inspired by sketchy stories more than four centuries of oral tradition removed. This is the same category that on many occasions the Bible falls into, like the exodus story (and i don't mean just the implausible/mythological parts, but all of it) it still a fantastic founding myth that works on many levels.
One reason Greek stories have had such impact is that they talk about aspects of human nature like love, power and ambition. Amusingly most people never consider these factors when thinking about unreliable narrators/editors, usually assuming only unwitting mistakes of copy and interpretation rather than intentional adaption to changes in dogma or political interest of later editors to portray the ruling dynasty by divine right as unbroken chain for example.
It would be foolish to assume there weren't intrigue during Biblical times, we even have examples of foreign meddling in the form of assignations. Interestingly, during the several hundred years of the Biblical "kings period" in each kingdom (Israel and Judah\Jerusalem) were ~20 kings and ~half of them were murdered, but while in Israel in each case this led to dynasty change, in Judah it never had (there is more shenanigans)
There is also a theory that the biblical 'united kingdom' was a fiction to provide narrative continuity along with Yoshiyahu attempted reform and turning Jerusalem as the center of ritual for the Jewish god. Note that at the time kingdom of Judah was backwater compared to the prosperous kingdom of Israel and there is basis to suspect that the ark of the convent resided there, but then Asyria conquered Israel turning it into its tributary, presumably leading to migration to Judeah, which resulted in some syncretism and the Bible setting on Judah\Jerusalem as being the center of all with backdated embellishments.
And I am just scratching the surface here..
Note that in Greek stories you also see progression as Titans, the former gods, replaced by a new Olympian order (btw iirc Titans represented the early Greek tribes but I might be confusing stuff with Egypt, it have been awhile). Despite some difference in narrative we seen similar thing in Mesopotamia as new empires and gods rise to power replacing older ones and become more universal through syncretism. Similarly in the Bible, early on you have many gods and polytheistic ritual (in both Israel
and Judea, some even represented by statues) with examples of ordalia and god/prophets convincing that the Jewish god can do what the other gods in the Canaanite pantheon can, the Biblical narrator use different literary devices than the Greeks but they serve the same purpose.
Otherwise, I can't speak to your beliefs and interpretation of archeological findings. Only that science wasn't kind to the pervading beliefs about the historicity of the bible, many understanding from past millennia's have been changed, today the vast majority of scientific community do not regard the Bible as historic document, and there are several events for which biblical narratives are considered as either fiction or have competing interpretation with at least as much evidence.
In summary, outside of things like whether the earth is flat, I don't think that there is any meaning to 'false beliefs' in the context of what we were talking about.