Are there actually students who learn by watching?
I am not an expert in cognitive science or psychology but I have a few years of teaching assistant experience behind me so I will have a go at this one and I suspect that a few others might even agree with me.

My general roles are in leading discussion sections and in lab sessions (information science: so combination of coding and data analysis in context with social science literature)

Now learning by watching aka observational learning is not a new concept. Scientists have been studying this for a long, long time. However, note the example literature cited in the previous links. There is a marked difference in learning how to strike a Bobo doll and acquiring a complex skill such as deriving Newton Law's of Motion

Having laid all of this expository work, I would like to argue that personally, I believe that observational learning exists and happens in the natural world around us. I just don't believe that one can acquire complex mathematical notions and concepts just by observing (unless this girl is some sort of a savant).

I think that this student was just trying to make you do her homework problems for her.