Difference between この and その As far as I know (I thought I knew), - is related to things that are close to the person who speaks, and - is related to the person who is spoken to. Is that right ? However, in a exercise book, I had to answer this: __(close from the interlocutor) I answered "", but the book answer says "", and I don't get why.

Your understanding of and is correct, I think the confusion comes from the wording of the question. As there only seems to be one person talking, you can assume that person is the interlocutor. So if the subject is close to the interlocutor (the person speaking), you would use .