It depends on how they say it. If they say it calmly and can move on to another thing to talk about then they really don't care. If they are upset or very emotional saying that they don't care, that could mean that they do care but they are trying not to care... they are trying to convince themselves that they don't care along with the person they are talking to.
I feel for you it means they want you to take control for a change:)
Usually. Sometimes I ask people who point out they don't care about one thing or another, "Then why did you bring it up?"
Not with me, it means I could take it or leave and pick up the pieces later.
I think most of the time, they really don't care.
it never means I care, and from what I've seen, it rarely means others care