I watch "SuperNanny"... every week! The same-age children in some of the shows are not unlike my own at times, and her techniques are helping us, when applicable.
But, if I had a doctor diagnose her as ADHD, I'd probably seek more information as well as a 2nd opinion. I've never heard ADHD considered a disability, and it's "in" our family: unfortunately IMHO used as a crutch. And I have what IS considered a disability, that most people would never question: MS. I'm one of the lucky ones, who has it but you can't tell by looking at me most of the time, so even I grow uncomfortable with being called "disabled" when there are so many who are worse off than I.
On another note: It seems to me that the parents of this child in the article could have better spent their money on specialized education, than on an attorney all the way to the Supreme Court? It isn't stated that I recall, but I doubt this case was free.
I think everything you said is very reasonable and intelligent. Your beautiful little child is probably just normal in the range of her specific personality type. I think you are wise to look for discipline adivce first. Some kids are more challenging, and sometimes it is just a matter of trying out different techniques and being firm but loving. Do not yield to her control no matter what, but stay calm and sweet. That whole eye contact thing is big, plus talking slowly and being very specific and very consistent. Three is very young. You have lots of time.