Q:

Theories with non-vanishing commutators outside the lightcone

I'm reading Weinberg's new book on Quantum Mechanics, and in Chapter 8.7 "Time-Dependent Perturbation Theory" he derives the usual Dyson series for the $S$ matrix when the interaction Hamiltonian $V_I(t)$ (interaction picture) is the integral of a local density $V_I(t) = \int \mathrm{d}^3x\ \mathcal{H}(x,t)$:
$$ S_{\beta\alpha} = \sum_{n=0}^\infty \left[ -\frac{i}{\hbar} \right]^n \int \mathrm{d}^4 x_1\cdots\int \mathrm{d}^4 x_n\left(\Phi_\beta,\ T\left\{\mathcal{H}(x_1)\cdots\mathcal{H}(x_n)\right\}\Phi_\alpha\right) $$
with his notation $\left(u,v\right)$ for the Hilbert space inner product. He then discusses when this formula is Lorentz invariant. There is no problem defining the time ordering when the $x_i$s are inside the light-cone, but the time ordering is ambiguous outside the light-cone. So the usual argument leads to the condition:
$$\left[\mathcal{H}(x,t),\mathcal{H}(x',t')\right]=0$$
if $ (x'-x)^2 \geq c^2 (t'-t)^2 $. So far so good - I've seen all this before. But then he gives this parenthetical:

(This is a sufficient, but not a necessary condition, for there are important theories in which non-vanishing terms in the commutators of $\mathcal{H}(x,t)$ with $\mathcal{H}(x',t')$ for $ (x'-x)^2 \geq c^2 (t'-t)^2 $ are canceled by terms in the Hamiltonian that can not be written as the integrals of scalars.)

There are no references for this, and as far as I can tell it is not clarified anywhere else in the book. If this is true it seems to contradict some of the arguments for local quantum field theories as being somehow a unique (apart from string theories) set of consistent relativistic quantum theories. Does anyone know the theories Weinberg is making reference to here?
(If it's string theory I guess I'll go listen to the Derpy song.)

A:

Probably, Weinberg means the instant Coulomb interaction term that appears in QED formulated in the Coulomb gauge (see his Quantum Theory of Fields, V. 1.)

