The most common and most likely answer to this crossword clue is the 9 letter word ANECDOTAL
I've seen this crossword clue in Independent
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More clues leading to the result ANECDOTAL
- Point in article on City almost entirely based on hearsay
- Dance a lot, jiving, according to the stories
- Located an oddball, according to tales
- Reported cane toad swimming on top of lake
- Tale can do with alteration as story
- A name located possibly regarding telling of story
- Note a lad busy around college with liking for narrative
- Unreliable NATO deal negotiated to restrict cocaine
- Loan cadet arranged, based on hearsay
- Cane toad hopping towards lake, so the story goes
Buddy explains!

The straight part
We know that "so the story goes" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case so the story goes = anecdotal.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does ANECDOTAL mean?
ANECDOTAL adjective- Of the nature of or relating to an anecdote.
- Containing or abounding in anecdotes.