Given how little we know about the Higgs -- namely, that we're pretty certain that at least one particle exists which probably behaves in the same manner as a H

Given how little we know about the Higgs -- namely, that we're pretty certain that at least one particle exists which probably behaves in the same manner as a Higgs boson would on several tests -- I'd hesitate to draw conclusions on the basis of how a particular model suggests that the Higgs field behaves.