It's not my specialty, so I don't know a whole lot about it. But remember that looking at things in a Higgs sort of way is quantum theory, and looking at things in a spacectime way is general relativity. There's no easy way to get them to match up unless we can develop a quantum theory of gravity. So the fact that the two ways of visualizing the situation are incompatible isn't too surprising, really.
As for the Higgs boson, it's like the photon and electromagnetism, more or less. You can either choose to talk about the electric field and the way it interacts with other particles and influences them, or if you'd like to explore it on a quantum level, you can talk about interactions with individual photons or virtual photons. You're free to take either a field view or a particle view, and which we do depends on what kind of problem we're trying to solve. In the same way, you can either look at the Higgs interaction as being a field or a particle, and which you depends on what you're working on.
At the very least, since dark matter has mass, it should interact with the Higgs field. It might certainly be tied even more closely than that. Notice that in particular the Higgs doesn't interact with massless particles, like photons, which is something very like the behavior of dark matter. I don't think it's possible for dark matter to simply be the Higgs boson, though, but I confess that I don't know the details of why not.
Originally Posted by EDG_
Conserve energy. Commute with the Hamiltonian.