She has simply not proven that people get smarter when they believe they can get smarter/have a growth mindset.
It is my understanding that the original research was regarding motivation. On one side was fear of loss of being regarded as "smart", concern over perceived failure, distaste for tasks requiring effort (eventually called fixed mindset). On the other side was what came to be called growth mindset: interest in trying new things, taking on a challenge, experiencing a learning curve (including initial "failure" and effort). The studies on motivation showed that those exhibiting the growth mindset learned more.
To do that would require...
While the type of study you describe, conducted by controlling the education of children in a manner which may cap the academic progress and intellectual growth of some children, may be considered unethical and denied IRB approval, others believe the implementation of common core and frequent measurements/assessments/testing are essentially changing US public schools into a lab to study these effects upon our children, in attempt to create equal outcomes for all.