As you know, I’ve done a bit of comparative vinaya studies, and I’m quite hesitant to conclude that origin stories were handed down together with the rules. It’s really not the case that the different schools generally have the same origin stories with just some minor variances in the details. For most rules, the origin stories are either generic back-formulations from the rule, or clearly distinct stories. Even for the heavy rules, such as parajikas and sanghadisesas, the origin stories mostly don’t match.
Only a minority of rules have the same origin story in most or all schools. Usually, this only happens for very memorable and entertaining events, such as the bhikkhuni rule that we are not allowed to throw trash over a wall, and it’s origin story about dumping feces on a brahmin’s freshly washed head.
Have you had a look at this? 6 different origin stories in 6 schools for the identical rule. The schools that have properly developed stories all describe different events.
Even if the story is very memorable and entertaining, and thus found in several vinayas, it’s not always applied to the same rule. For example, the story where bhikkhunis build a stupa, a monk is annoyed, smashes the stupa, and then the bhikkhunis have some kind of drastic reaction to that, is also a very elaborate narrative that is found in non-Pali vinayas, with lots of variances in the details. In the Pali tradition, this story is paired with the rule about not abusing monks (pc52). In other schools (Dg, Mi, Sarv, Mu), it’s paired with the rule about not entering a bhikkhu monastery unannounced. In Dg, both rules are tied together by one continuous origin story. The Mg doesn’t have the story at all.