One of the most well known stories about Archimedes is about his Eureka moment. In the story, Archimedes is asked to figure out whether or not a crown is made of pure gold or not. Initially he is stumped, because he doesn't know how to determine the volume of the irregularly shaped crown.
A few days later, while he is taking a bath, he notices the water level rise in his bathtub. Archimedes realizes that he can measure the crown by submerging it in water and seeing how much volume is displaced. He swiftly jumps out of the bathtub and shouts "EUREKA!!" ("I've got it!").
This story seems to be the source of the popularity of the phrase "Eureka," and the inspiration behind "Eureka moments." So, did this story really happen? Is this a historically documented event, or is it just a nice story?
It's not like you are going to find any archeological evidence regarding the matter, so the historical documentation (Vitruvius, living ~200 years after Archimedes) is just a nice story.
I'm not really sure what you are getting at - the account certainly does sound fictional but so does much of what we "know" about Archimedes outside of his own works (using mirrors to burn ships, the manner of his death, etc).