I am currently interviewing in several universities across the U.S. for PhD programs in computer science. In every one of my interviews so far, there are always 1 or 2 professors that are eager to know which specific problems I am interested in researching (and it normally comes out as the most important question they are going to ask me). This question stumps me every time because I am not trying to enter a PhD program and start working on a specific problem right away. Instead, I want to do some lab rotations first and get a deeper feeling for the work of the institution's faculty (that works on my subarea of interest) and then, after these rotations, pick a specific problem (perhaps this is the wrong motivation?).
It does not seem to me that interest is a reliable determiner of success in completing a PhD. I could say that I am interested in Dr.X's research on complex manifolds because I skimmed through some of his papers. However, from my personal experience, I think there is a very big discrepancy between having read a little bit about a topic and claiming it as an interest, and actually doing research in that area. In other words, one might be interested in doing research in modelling the response of cancer patients to drug Y (because they want to defeat cancer or something similar) but a lot of times that person might realize that the actual research is far from his expectations and end up switching to different area.
I could list a few other reasons why I think interest is not a good measure of student's commitment but I might be wrong since professors like to ask this question. Why is this and what would be an honest way to answer it?