how can a story be real but also not -> it all happened, just not how it was said to have happened is actually very very very interesting re: summer when you think about what we've been told about her story, specifically how the characters believe it all went down.
summer leaves on a mission to face salem alone -> summer leaves on a mission to face salem but she wasn't alone, she had at least raven with her. [this is basically the proof of concept. the story of summer we've been told so far isn't a complete lie, but there are parts we are not yet aware of.]
summer dies on said mission -> this is where it gets interesting, bc if this did happen but not in the way we think, then... how? did summer die and was brought back to life somehow—hence raven's "i know people who can come back from the dead"—or is this a "by all means this should have killed her but didn't", e.g. summer fell into a grimm pool and had the same happen to her as what happened to salem, and the assumption that salem only survived bc of her immortality and the pools are lethal to everyone else is wrong, the pools simply don't kill bc that's not what destruction is really about [destruction fuels creation. if ambrosius must destroy his previous creation to create something new (which in fairness is light's view of the balance, which is kind of.. skewed), destruction with a side of creation would basically be change.]
meeting summer gave salem an idea for her experiments which would lead to the hound, and summer was her first test subject -> i think it's safe to say it's true that salem went from hunting down and killing silver-eyed warriors to capturing them somewhere around the time of meeting summer, but summer being her first test subject, the first "hound", can be contested. and frankly, applying "it happened just not the way they said it did" to "summer was the first hound" gets us right back to the "summer fell into a grimm pool" point; if summer is grimmified in any way shape or form, then it likely wasn't due to any kind of experimentation but a happenstance that gave salem the proof that this was doable in the first place [further experiments might prove that there's more to it, i.e. every grimm fusion so far involves having some type of magic as well. compare cinder's grimm arm and tyrian's regular prosthetic; why the difference?]
...does this make sense or did i lose the plot rambling too much? i will never know.