What is the difference between whether an employer is an agent of an insurance company or the agent of the insurance company?

I have read a number of the United States cases. I am again reminded of the words of Taschereau J. in Provident Savings Life Ass'ce Society of New York v. Mowat et al., at pp. 152-3, "this is a class of cases where the rule cannot be too often recalled to attention that general expressions in every judicial opinion are to be taken in connection with the facts in reference to which those expressions are used". That principle may explain to some extent the conflict in these cases. Each case must stand on its own factual base. Whether an employer is the agent of the insurance company or the agent of the employee in a given circumstance depends upon the factors to be determined, all of the facts and the relevant documents including the group insurance certificate where applicable, and the relevant responsibilities thereunder.