"Granny claimed that someone in the family, maybe her SIL, got her breast caught in a wringer."
Oh it did happen.... Bosoms, fingers, arms, hair, a man's tackle, anything too near a wringer/mangle was fair game to be sucked into those rollers.
Trip from corsets to modern brassieres was a bit long. And what passed for later early on were really nothing more than bits of fabric sewn onto straps of a sort. Even then many women either out of financial necessity (couldn't afford), or personal comfort didn't wear the things indoors.
If you could only afford one or two good bras, most women kept that bit of gear off indoors, and saved it for when they had to go out.
Women's clothing (especially house dresses) being often of loose material could easily get caught up in a wringer or mangle if a female leaned too close. Once that happened we all know results, mangle/wringer would keep pulling in whatever object until stopped.
With hand powered mangles/wringers getting body parts or other things caught up was less of a worry. One simply stopped operating mangle and that was that.
Introduction of powered wringers/mangles introduced a whole new level of threat to safety. Hence those devices either by regulation or manufacturers themselves (perhaps wary of being sued out of existence), incorporated safety releases.
Post war USA at least as more automatic washing machines arrived on market drum beat from consumer testing and other media was clear. Wringer washing machines were dangerous and should be consigned to rubbish bin of history. By 1960's this drum beat grew louder with voices joined by doctors and others.
https://www.discovermagazine.com/the-sciences/ncbi-rofl-no-bra-wringer-washing-machine-squished-boob
https://www.researchgate.net/public...ing_Machine_An_Unusual_Cause_of_Breast_Trauma