Can a CRNA be medically directed and be an independent contractor for tax purposes at the same time?

Employee or independent contractor designation has significant tax implications for the Certified Registered Nurse Anesthetist (CRNA). On superficial view, it appears that a CRNA who is medically directed would be under a number of controls that would force the CRNA to be in an employee status. However, on analysis, it seems that for tax purposes a CRNA can be medically directed while also being an independent contractor. But when looking closer at all of the controversy in the legal system and the protections available to an employee that are not available to an independent contractor, a CRNA may find the employee status a better option.