Lore does say this now. But no, I'm not conflating Nero with Da Vinci, because I remember that part on her from way before F/GO came out. Like, a year or two before that, if not earlier. However it wasn't stated outright, and could be a fan theory I heard or read about. It was about ten years since then after all.
I can only assume it's a fan theory or from a fanfiction based on Imperial Privilege allowing her to take on the "burden of the body" of skills she takes on because I sure don't remember that anywhere in Extra.
She's canonically a Saber class servant because of Imperial Privilege but it has nothing to do with her gender.
IIRC Jackie's excuse is the same as Sasaki Kojiro's - the actual Jack the Ripper is as much a narrative construct of the newspapers as a specific person, there may have been an original killer, but they weren't any more exceptional than the copycat killers and misattributed deaths.
So the summoning got the closest thing that fit - the collective spiritual amalgam of those who died on the streets,including the criminals and human predators that haunt the night and the omnipresent deadly pollution thats never noticed until it kills someone, all blended with a mix of the fears of the time.
Really she's as much a story as she's a ghost.
No, Jackie is almost the exact opposite of Kojiro. There are canonically multiple unrelated Jack the Ripper servants on the Throne because of the unsolved nature of the Jack the Ripper murders. Unlike Kojiro who didn't exist so the Throne grabbed the closest possible match and just called it Kojiro.
Jack the Ripper absolutely existed but what got enshrined in legend wasn't what Jack did but the mystery and the fact they were never caught so the Throne grabbed multiple entities active at the time who had the potential to genuinely be Jack the Ripper and enshrined those.
Jackie is a conglomeration of the grudges of London's unborn children either taking the form of a little girl who was never born or possessing a street urchin who did exist (the exact details are vague and slightly contradictory between original LN and now). She was eventually exorcised as a wraith by a mage of the time which is why she dislikes mages.
The mist is an ability she had in life based on instinctual magecraft that got mixed with the pollution of London when it became a Noble Phantasm. The only currently known direct effect of the Jack the Ripper legend on her is what she calls herself, possibly her clothes, and her From Hell letter in her valentine. She's almost all ghosts (plural) barely any story.
The one you're possibly thinking of is the Strange Fake Jack which is an entity representing "The Mystery of Jack the Ripper" in a similar situation to Nursery Rhyme. That Jack is "all story, no ghost" but is explicitly separate from the apocrypha Jack we call Jackie.
Notably neither of the currently known Jack the Ripper servants actually know the answer to the mystery of the Jack the Ripper murders. SF Jack because of the nature of its existence, and Jackie because she wasn't paying any attention to that at the time.