You're assuming Terri had the ability of rational thought.
If she didn't have rational thought before she collapsed, why did Greer "find" that her words "no tubes" had importance?
You bring up an interesting point. I've wondered if Greer asked any probing questions about Terri's state of mind at the time she allegedly said "no tubes." Was she depressed? Was she obsessive? (Michael thought she was obsessive about her weight). Was she fully informed that her words could kill her?