In 1992, M W Evans proposed a so-called O(3) symmetry of electromagnetic fields by adding a constant longitudinal 'ghost field' to the well-known transversal plane em waves. He considered this symmetry as a new law of electromagnetics. Later on, since 2002, this O(3) symmetry became the centre of his Generally Covariant Unified Field Theory which he recently renamed as ECE Theory. One of the best-checked laws of electrodynamics is the principle of linear superposition of electromagnetic waves, manifesting itself in interference phenomena. Its mathematical equivalent is the representation of electric and magnetic fields as vectors. By considering the superposition of two phase-shifted waves we show that the superposition principle is incompatible with M W Evans' O(3) hypothesis.