This statement is related to the fact that renormalizability of a theory depends of the mass dimension of the coupling constants in the Lagrangian. Couplings with zero or positive mass dimensions lead to renormalizable theories. As a consequence, writing down only terms with appropriate mass dimensions is required in order to construct a theory that is renormalizable.
In quantum electrodynamics, all operators consistent with both (local) gauge and Poincaré symmetry that are at most of mass dimension 4 automatically satisfy the above criterion. One could understand the statement in the reference in this way. Of course, this does not hold for term of higher dimension.
This post imported from StackExchange Physics at 2014-05-04 11:28 (UCT), posted by SE-user Frederic Brünner