Interviewees should act in a humble manner and have several (at least two) methods of obtaining these materials to offer the "principal." In my particular case, my principal had taken away my students' rights to check out library books because too many students were not returning the books. I was asking that this be reversed or that an alternative was found. I suggested to the "principal" that we 1. Refuse to hand out report cards to any students who have not returned materials 2. To create an online database (reflecting those of college campuses) that would allow students to access library books/materials without having to check anything out etc. It is very important to be humble, and reflect on the fact that you realize that the principal has a lot more experience than you, a first-year teacher, but that you are dedicated to finding a solution that will work for both parties.
I had to role-play a situation where my principal would not allow my students to take home library materials in order to finish research for their term papers (4th grade... I was being ambitious. ;-) My goal was to convince her to let them have more access to the materials.
I described the situation and asked her to clarify it for me. I then asked for her advice (huge in education administration), and adapted her statements to fit within a plan that would allow my students to have the books in the classroom. Essentially, I led the principal to thinking that she had helped me to develop the answer, which created buy-in. When I offered to do all the leg work with the librarian, she had a win-win situation (and so did I). My interviewer was very impressed that I could both flatter the principal, "seek her advice," and still get what my kids needed. She said that my ability to speak through this negotiation process and how I approached the situation was more important than my actual answer. I.E. how you think is more important, because that means you'll be able to solve the problems that come up as you teach.
Teach For America doesn't want teachers who are patronizing. They want to hear that you still have high expectations for students regardless of their situation. Obviously, if you weren't empathetic to children living with poverty, you wouldn't (or shouldn't) be applying for this position. It is a poorly worded question (ha) so you have be careful with your word choice in your answer.