Whether someone is an employee vs a contractor solely depends on the "economic reality" of their job. Neither the employer nor the employee can choose to have it classified as a contractor relationship if it isn't actually one.
For example, if Subway determines how, where, and when I make the sandwiches, and provides all the equipment and materials, then I am a de facto employee. Even if both Subway and myself voluntarily agrees that I am a contractor for whatever reason (sidestepping minimum wage laws in this case), and signs a service contract to that effect, I am still treated as an employee under the Fair Labor Standards Act.
[0] https://www.dol.gov/whd/workers/Misclassification/misclassif...