Ficticious forces in non-inertial coordinate systems do not have action-reaction pairs. For instance, there is no reaction force to the centrifugal force in a rotating reference frame. So adding the ficticious centrifugal force helps Newton's 2nd law to work, but causes Newton's 3rd law to fail.
I certainly would not make such a statement. The fields carry momentum and store energy so trying to claim that they do not exist will ruin all of your conservation principles. I don't know what criteria you would use to say that they don't exist.
EDIT: On the other hand, they are frame variant quantities. In that sense they are more like energy or time than mass which is invariant.