This belief is actually well founded, because Katie does believe in the resistance, heart and soul. As she tells Broussard, the only people she puts above the resistance are her family, including Will. And Broussard is apparently willing to accept that, to the pointing of excusing Katie's killing one of Broussard own resistance guys, to save Will.
Quayle isn't willing to accept anything about Katie now, and this sets up a nice complexity in the cental conflict in the series: not just two sides, but sides in which different members have what amount to sharply different views. Katie and Will ultimately want to the same thing - a world free of the occupation (whatever exactly that is) and collaborators - but go about getting this in different ways. Katie knows more, and therefore holds more of the cards, than does her husband. And now we have this tension between Quayle and Broussard.
All of this is simmering backdrop for the urgent matter at hand: the search for Broussard, by Will and the forces of the occupation he commands. Katie has already shown that, not only will she kill a resistance man to save Will, she will tip off Broussard to save him from Will's forces. Walking this fine line isn't easy, and adds a continuing dollop of tension to every scene.
It's good to see Tory Kittles, who put in a few good years in Sons of Anarchy, in the important part of Broussard. As for the series itself, I'd still like to know a lot more about the occupiers, but the story is sufficiently good at this point that I'm willing to wait.
See also Colony 1.1: Aliens with Potential ... 1.2: Compelling ... 1.5: Questions ... 1.6: The Provost
not exactly aliens, but strange enough ... The Silk Code