I think we are supposed to believe that the Sims in Woodbury are stupid enough to have some kind of investment in Andrea, after her little speech and all. If she had refused I have no idea what he would have done, it isn't well written, you forget. So the Governor can't just have his henchmen off her in the streets in front of everyone, he has these people convinced that he is the good guy.
They are taking Andrea to teh meet, they would have wanted her armed if they really thought she was... you know what, fuck this show, I am not putting this level of analysis into it. Just fuck it.