I actually thought that Andrea had the smarter approach. It's like, if someone has you in captivity (not quite but basically) why are you going to have attitude? Why not play nice and see if you can manipulate the situation to your benefit? Of course you don't actually trust or like the people you're around, but you play nice so you can see ways that you can manipulate them. At least until you learn to trust them and vice versa. Michonne was definitely right not to trust the governer, I just think she shouldn't wear her heart on her sleeve quite so much. I would have been a sweetheart to all of those boys to get them to think I wasn't a threat. Then, if necessary, at the right moment you do the unexpected and slice their heads off.
I actually think Andrea is a victim of the trappings. She sees a town, people, food, place to stay. This handsome man with power. I don't think she's taking your approach. I think she might be crushing on "govie". Which is what Michonne senses I think. Some women are like that. I think this community was light in her darkness. She's been separates from her own group, hasn't had food or a place to stay in months. She is being seduced by the situation. Reminds me of that old story about the witch who fattens up kids so she can eat them. The kids are unaware of the danger they're in because all of that good food is in front of them.