Closed-ended testing is standard for Gifted and Talented programs throughout the country. Are you saying that she did not meet the requirements using those tests?
To make matters worse, it's quite common for very gifted students to also have issues like ADHD or OCD, which qualifies them for a label of twice exceptional. When I was raising my now adult sons, schools typically wanted to label a child either gifted or special needs and often seemed incapable of comprehending that a child could be both.
I ended up homeschooling and as a consequence I was involved with an online voluntary health and welfare organization for the gifted. My impression was that it was pretty common for people with very gifted or twice exceptional children to homeschool due to frustration with how schools handle such students.
They need custom help that few people are qualified to adequately provide.
Edited because: autocorrupt.
I'm going to have to steal this one. It gave me a big chuckle!
They did the same thing with reading: don't give a student the chance to show higher proficiency, and you effectively cap the level a student can be 'assessed' at.
We took our kiddo on a trip to Colorado to the Gifted Development Center which was a good helpful first step (and connected a lot of dots for us). More than happy to share experiences at matt at mindvault dot com.