They said she’s legally dead. What does not mean? How can a person declared dead with certificate of death if she’s still on ventilator? Youtube? Yeah? But still on ventilator!
Did you watch the video I linked? The physician in that video explains very well what brain death is, and why the heart continues to beat when the dead person is kept on the respirator. If you remove the heart from the body and supply it with nutrients and oxygen (and possibly carbon dioxide, but it probably makes enough on its own), it can survive and continue to beat for a long time. That does not mean that the person it was removed from is alive.
Everything that makes you who you are is in your brain. You are aware that you are alive because of your brain. When the brain goes, you are gone--regardless of whether the rest of your body dies along with the brain or later. Jahi's heart has been kept beating for an unusually long time after her death, but that does not change the fact that she is dead.
I do not know what the family is doing with the corpse now, but this is gruesome horror-movie type stuff. The family's state of denial should have never been allowed to go this far.