The "bare minimum" required by law is still "doing whatever is required to save you life". They cannot legally kick you out if you are not stable.
Thing is the state hospitals will actually try to cure you; and they are fairly good at it. Harborview (part of University of Washington) is the only L1 trauma center in the region.
For-profit hospitals stick it to the taxpayers by doing this. It's a good argument for some form of universal healthcare, since we're paying one way or another.