Determining whether someone is an independent contractor has always involved multiple factors. Flexibility of working hours is just one of the factors.
You cannot say categorically that having the ability to choose your own hours makes you an independent contractor rather than an employee.
Other factors include:
* What level of control does the employer have in dictating HOW the work is done?
* Is the worker performing work that is outside the usual course of the employer's business?
* Is it customary for the work to be performed as an independent trade?