Still wrong. Oil and water stratify too. I guess that means its okay to dump some coolant into my engine if I don't have a quart of 10w-30 laying around.
Correct. They do not mix.
and you might logically conclude it's not a good idea the put them in the same system if it can be helped.
Since the characteristics of both are different - in some ways opposite - having both in the same system would generally be counterproductive.
Rick E-berg has posted that military vehicles running SBBF have a sticker like this.