There is a common belief that canonical LQG techniquesalways result in the construction of a quantum dynamics which is unable to propagate perturbations from one vertex of a spin network state to another. I will describe the rationale for this belief and show that contrary to this belief, LQG methods can be consistent with a propagating dynamics. I will demonstrate this in some detail in the context of an LQG type quantization of a weak coupling limit of Euclidean gravity.