"And, we don't obtain the right to pull the plug"
What plug would they be pulling? It's not like they would be shutting down a respirator or anything like that. The only thing they would be pulling from her is her food supply. "Pulling the plug" and literally starving someone to death are two completely different things.
Yes, you are right. Pulling the plug means someone is brain dead (at least that is what I believed it meant - might mean anything now with the happy/healthy crowd making decisions for the plugees).
Withdrawing the tube is starving someone. This is a cruel two week process that is not an easy death. If you do this to her, what about withdrawing feeding from children who cannot feed themselves? What about any number of "what ifs"?