Reinforcing their beliefs might work for making them even more insane.
Honestly, it would surprise me if either of those strategies worked (or failed) as one might naively expect, since I mostly expect pathological delusions to involve some seriously atypical connections between observations and conclusions. But I bet there's people on LW with experience in the field, or at least who have read up on case studies.
Rationality quotes time!
The usual rules: