No, it isn't. Volunteering, helping friends and neighbors and cleaning your house are examples of services provided without the profit motive.  One of the reasons the Canadian system is cheaper is because it runs at cost without having to make money to give to shareholders.

I might add that I have no problem with profit in many sectors and was actually in business myself for a long time. The evidence is that the American system costs more however, and profit is a significant cause. Someone unlucky enough to need medical attention should not end up broke so someone else can profit.