Saved?

Well, no.  It was in a skip in the harbour master's yard.  It wasn't exactly thrown out with the bathwater but did that happen? In mediaeval times people shared scarce bathwater and by the time the baby was bathed the water was so murky that the baby was in danger of being thrown out unseen (probably nonsense). Nowadays the phrase is used to mean don't get rid of the good parts as well as the bad parts of something when you are trying to improve it .