Dead is not the right word. Non-functioning, maybe. Her personality has been forever compromised because of her brain damage, her selfness is not and will never be the same (even if they could replace the brain tissue with stem-cell therapy, she would never be the same Terri.)
Dead shows your own set biases.
It is ok if in your system of beliefs you say, "Her brain is damaaged past the point of her having any sense of self-awareness, and her personality is destroyed, therefore I believe her body should be killed because it is not desirable to to on like this," but to say she is dead is also a value judgement not based on reality, and reflects a distancing that makes it easier to excuse euthaniasia in that condition.
In reality, she is alive, and with some nursing and being fed she could live quite a while like that.
All of us have come into this with our own distaste of something about her case. If she were my child, or spouse, I would have kept her alive, in honor of that spark of life, although I might have refused having her resussitated in the first place, because she was dead from the heart stoppage. If she were yours, you would well be within your rights to seek ending that life.
I'm hair-splitting, perhaps, but I just don't feel it's right to call someone alive, even if badly damaged and not likely to get better, dead.