It may be a bit more complex than that. Idiomatic phrases, adages, maxims, etc. can enter the language through a variety of avenues. Some of them come from actual events, some come from stories or legends, some come from observations or common phrases in a specific profession or field, some are just clever observations or re-phrasings of "common knowledge", some are pet phrases of famous figures or authors. Others come from songs or poems, etc. etc. Some even enter the language from foreign languages, although it is also quite common for two separate cultures to make highly similar observations, or have essentially identical phrases.
Mandarin Chinese for example has "to kill two birds with one arrow", which may or may not have been borrowed. English uses the phrase, "waiting for something to fall into one's lap", or "out of the sky", Mandarin again uses a very similar phrase, but the thing falling is a meat pastry. Go figure.
It is really quite involved and complex, you could write a whole paper on it (or book, if you were more enterprising).