The oil and water pumps are actually separate, though both live in the same housing. There is a tell-tale hole in the pump case, facing downwards, and, unfortunately, many times we have heard of the hole being blocked solid with crud. This then can cause the weeping oil to be pushed into the cooling side as the mechanical seal on the water pump only resists leakage in 1 direction (from the inside towards the outside). The oil will always be pushed into the coolant as the pressure is higher. So yes, it may be that this is the reason for oil in the water, though it is not the only way it can get there. Look for the hole and clean it out with a drill bit, there are pics on the forum of this. Then, if oil weeps from the hole, a pump rebuild will be necessary.