Will a non compete agreement come in the way of pursuing employment with indiect client?

I'm employed with company A with whom I have signed non compete two years ago. I'm now consulting with company C through company B. C pays B, B pays A and A pays me. There is no direct relationship between C and A. Company C offered me a position and now company A says I cannot join because of non compete clause. C is big software company of about 5000 employees and A is about 30 employees. They are not competitors in any way. A is a body shop which provides software consultants. Is non compete still applicable even though A and C don't compete with each other? It seems like non compete is there to restrict employees from taking up employment with end clients. Please help.