I don't see a real downside to disclosure either. Well, actually I can think of one. It's possible the Sympathizers have the ability to disrupt our work, possibly by blocking an individual. In that case disclosure would help them. But that seems unlikely enough that catching them in lies will be a much bigger upside.
So, I have a specialty in hunting. I don't think anything that's come up so far will work towards that, so I'll just go wherever we need a number.