The Kootenay Doukhobor Historical Society v. The Queen case illustrates quite well that even if a non-profit and a staff person agree that the staff person is an independent contractor, there is an independent contractor agreement, and the staff person has considerable latitude in carrying out the tasks, the staff person can be found to be an employee. It is vital that non-profits and charities properly categorize staff. Failure to consider someone an employee when they really are an employee, and failure to withhold EI, CPP and income tax amounts, can result in considerable liability for a non-profit or charity. As well, directors of the non-profit or charity can be on the hook for the outstanding amount and this is probably the most common reason that the directors of a non-profit or charity would ever have personal liability.

To understand CRA’s position you should review RC4110 Employee or Self-employed? at 

Here is the full case of Kootenay Doukhobor Historical Society v. The Queen: