Well, as I said, I was trying to simplify the explanation to make it easier to see the difference.I think it's a little more complicated than that. The Usenet Physics FAQ has a good page on virtual particles and how they mediate forces:

http://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html

Also, since photons are their own antiparticles, there is no real difference between "emitting" and "accepting" one. With real photons, ones we actually observe, we can finesse this by decreeing that the earlier event is the "emission" and the later one is the "reception" of the photon, and since real photons go at the speed of light, which event is first is the same in all reference frames. But virtual photons don't have to move at the speed of light--they can go faster, or slower, and if they go faster, there is no frame-invariant way to say which event is first. That's why it's normally just said that virtual particles are "exchanged".

I kept typing "exchanges" but decided to go with 'emits' and 'accepts' to try to get across the concept in a way which would let him build a more complex understanding later.

Well, I wouldn't call string theory a candidate quantum gravity theory, but my understanding is several years out of date, due to being unwilling to seriously accept certain assumptions in stringy models. I'd say it's just an interesting mathematical structure from which certain interesting results can be produced.But from a quantum standpoint, the local spacetime geometry has to be quantized too, and when you try to do that, at least in the "obvious" way, you do get masses interacting by exchanging virtual gravitons. (I realize that is not a complete picture and there are a lot of issues in this area, which is why we still don't have a good quantum theory of gravity. But even in the current candidate quantum gravity theories, such as string theory, you still have virtual gravitons being exchanged--in string theory, they are among the simplest string states.) The difference is that, while there are positive and negative electrical charges, there is only one kind of "gravitational charge", since that is just energy, and the energy of gravitating objects is always positive--more precisely, the stress-energy tensor always satisfies what is called the "weak energy condition". (I think that's the right one--but experts, please correct me if I've misstated it.)

You can't perform renormalization on gravitons either.

The weak energy condition just requires that all observers find a non-negative energy density, which could be an argument against anti-gravity except others have found it doesn't preclude it by itself.

Indeed, I was trying to find a way to explain this, but you did it excellently.There is one exception to that generalization: "dark energy", which is energy associated with a cosmological constant, or, equivalently, associated with what we normally think of as "empty space". The stress-energy tensor of dark energy violates the weak energy condition, which is why dark energy can cause the universe's expansion to accelerate (a kind of "gravitational repulsion"). But dark energy has nothing to do with antimatter, and the special properties of its stress-energy tensor can't be possessed by the stress-energy tensor of any "normal" kind of substance, whether it's matter or antimatter (or light or anything else).