The longer I think about it the more convinced I'm getting that, if Gretchen was the spring maiden, she got involved in Summer's mission somehow and that led to her death? (My current theory is also that Summer used the first question in the lamp, but the specifics don't matter so much, just that spring was involved). A training accident never cut it for me as an explanation for what happened to her, but I would have thought if it was a lie and if Oz was going to come clean about this it would have most likely been in the whale during v8? Like sure you're still hiding things from everyone else but I would have expected him to at least explain to Oscar the real reason Hazel hates him so much given the circumstances. What if he actually doesn't know the full story himself for once?
what gets me is that, in what happened to gretchen, we only have ozpin's word—one that was only heard by oscar—to go by. hazel obviously blames ozpin, and he allied with salem because he believes she has a vision of world with no kingdoms and no huntsmen academies, but i can't remember a moment where hazel actually talks about what happened to gretchen, and thus we have no way of really knowing if it lines up with what ozpin is saying or not.
perhaps fittingly, hazel does say this on monstra: "nice story. but if gretchen's death taught me one thing, it was never to trust you." of course this isn't in response to anything gretchen related, but if there's something afoot with her death, well. it's a pretty telling line.
it's not unheard of that a student could die on a training mission—a signal student died (and that caused the teacher in-charge of them to resign), and yang almost died on a mission she should not have been on in a first place as a first-year student (which does not help ozpin's case here)—but there's definitely this feeling that something's up with gretchen's death, especially with how choice comes up alongside it; pyrrha was said to have made a choice too, but it wasn't exactly an informed, let alone 'no-pressure' one.
it's possible ozpin doesn't know the full story, but if gretchen was the spring maiden, it's an easy conclusion to come to that her presumed death had something to do with that. the 'training accident' explanation alone could be a cover-up to some extent. it could also explain the discrepancy: gretchen died on a 'training mission' and the spring maiden 'ran away', and if ozpin doesn't know what really happened to gretchen (but has his suspicions because she's a maiden and missing) then it's better to muddle the truth instead of connecting these two events and risk the information getting out. else the next thing you know, everyone is looking for gretchen rainart and if she's not already dead, then the chances are she will be soon.
it'd be a bit convoluted way to go about things, but it's not impossible. (it's not like the inner circle is ensuring that the maidens have a proper support system or anything. they're pretty alone out there, so hey, what's possibly-sorta-kinda faking a death of one in an opportune moment gonna matter? no need to get their family involved too.)
and if there is more going on with gretchen's death, then connecting it to summer's mission would make sense. hazel's dead so there's no reason to talk about it for closure, so the other option is to tie it into something really important... and maybe learn if there's an alternative, narrative-only meaning behind the "no more gretchens" line.