As I understand it the strong equivalence principle is the statement that within a infinitesimal neighbourhood of any spacetime point all physical interactions (gravitational and non-gravitational) follow the laws of special relativity. This therefore implies that gravitational energy should interact with gravity identically to all other forms of (non-gravitational) energy, in particular, it should "fall" at the same rate as all other forms of energy in a gravitational field. This enables one to extend the equivalence principle to objects whose graviational binding energy contributes significantly to their mass. (Please correct me if I'm wrong on this).
My question is, in what sense to scalar-tensor theories of gravity violate the strong equivalence principle?
Take Brans-Dicke theory for example. By promoting Newton's constant to a dynamical scalar field it is said to obey the Einstein equivalence principle, but not the strong equivalence principle. Is this because the scalar field only couples to gravity and not to matter? It couples to gravity non-minimally and in doing so the gravitational self-interaction of a massive body is affected not only by curvature of spacetime, but also the behaviour of the scalar field. Hence, all non-gravitational energy obeys the equivalence principle since it follows the geodesics of the metric, however, gravitational energy does not obey the equivalence principle since its interaction depends on the behaviour of the scalar field as well as the metric. Would this be correct at all?