I don't know, without examples, whether I would have trouble with what your person is telling you or not. But, I think what bothers one the most is our own thinking/believing that what we are hearing is odd and unpleasant to us and not knowing what to say, either way. It does not really matter whether the other person wants reassurance or not; we don't know what to say, period, because it is odd/bizarre/uncomfortable hearing for ourselves.

If someone prefaced something with, "Do you think this is odd. . ." and told me something I did indeed think was odd, I'd just say "Yes," and change the conversation. If it was something I did not enjoy hearing, I would maybe elaborate some and say, "Yes, I think it is odd and I don't enjoy hearing about this sort of subject," and change the subject.

I would never comment on the person and what I thought of them for doing/talking about the subject or presume to know why they were telling me what they were telling me but I bet that after a few switches of the conversation, they would find someone else to tell their tales to. I would not express any emotional displeasure (as they may be enjoying my discomfort) but would be a bit "stern" but matter-of-fact in my emphasis on not wanting to hear anymore.

If you otherwise need to work with this person or like them okay, I would make sure that you express those emotions (compliment them, smile, otherwise talk with them during spare time) so they "learned" to differentiate subjects you did not enjoy from those you did not.