I'm also confused why they drop this point. I don't give in to this kind of threat because I expect overall a policy of giving in leads to worse outcomes.
Act utilitarians specifically don't believe in evaluating the overall consequences of a policy. Rule utilitarians do that. That is, in fact, the major difference between the two.
Good point, I phrased it poorly. Because of the effects of the specific action, I think an act utilitarian should still refuse to be mugged in this case.