I don't know why she didn't just say no.
Just a guess as to why...
Some of the text during the video explains that it is legal for agents to lie but is ILLEGAL for people to lie to agents. I don't know the legal reference, but from what I recall that is correct.
If she was to say "no" and that was the truth, there would still be the possibility that somehow the agents would be able to make a convincing case that her answer of "no" was a lie (even if it was the truth).
By not giving any answer at all she could never be charged with lying (legitimately or illegitimately) since she never gave an answer at all.
What made me think that might be why she wouldn't answer is the following YouTube video: http://www.youtube.com/watch?v=6wXkI4t7nuc (the video of the law professor who explains to his class why they should never talk to the police).